derivation of area of parallelogram

Derivation of the law Note: All the letters in bold represent vectors and normal letters represent magnitude only. The area of a parallelogram is given by Area of parallelogram = Area of Rectangle. Explanation: . The area of a parallelogram is the number of square units inside the polygon. Area of parallelogram = Area of Rectangle. It is a quadrilateral wherein both pairs of opposite sides are parallel. In the above picture, we need to show that the area of parallelogram ABEC has the same area as the rectangle ABFD, which is bh. So the area of the parallelogram is Since this is the area of two trapezoids we have to divide this by two, giving Finally.. The area of a parallelogram can be determined by multiplying the base and height. Area of Parallelogram is the region covered by the parallelogram in a 2D space. sinα = h / b; h = b; A = ah; A = ab. b vector = 3i vector − 2j vector + k vector. A parallelepiped is related to the parallelogram in the same manner how a cube related to the square and a cuboid related to the rectangle. Monday, 14 December 2020 / Published in Uncategorized. 2. Page 5 of 7. To better our understanding of the concept, let us take a look at the derivation of the area of square formula in maths. Also, derive the area analytically and verify the same. An alternative proof of the area of a trapezoid could be done this way. This page describes how to derive the formula for the area of a parallelogram. A parallelogram area can be calculated by multiplying its base with its height, i.e., b x h. The height of the parallelogram must always be perpendicular to its base. 4:46. Parallelogram inscribed in a quadrilateral, Perimeter of a polygon (regular and irregular). Updated: Oct 15, 2015. pptx, 251 KB. To answer this question, we must find the diagonal of a rectangle that is by .Because a rectangle is made up of right angles, the diagonal of a rectangle … 4 years ago | 5 views. It works by moving a piece of the parallelogram so as to make a rectangle with the same area, which is easier to calculate. Find the area of the parallelogram whose two adjacent sides are determined by the vectors i vector + 2j vector + 3k vector and 3i vector − 2j vector + k vector. Now we replace C with pi times diameter: And replace d with 2r: Problem solving with Plane Area We can derive the formula by using the following steps: Draw a parallelogram whose base is b altitude is h. Cut a triangular shape from the parallelogram. Playing next. 4 in. so as to make a rectangle with the same area, which is easier to calculate. In this activity you are going to explore the area of a parallelogram, and how we can work out the area of any parallelogram. Area of Square Formula Derivation. Geometry lessons. The area of a parallelogram is twice the area of a triangle created by one of its diagonals. Subscribe to feed Thus "area"(ABEC)="area"(ABED) + "area"(ACD) ="area"(ABED) + "area"(BEF) ="area"(ABFE) =bh This constructs a rectangle by definition of a parallelogram. This site was created in a private capacity and is not the work of my employer. Deriving the Formula for the Area of a Parallelogram - Wolfram Demonstrations Project. Draw a parallelogram. Parallelogram decomposed and recomposed into a rectangle. And how we can define it. Assumed knowledge: Area of a rectangle This rearranging has created a rectangle whose area is clearly the same as the original parallelogram. Or if you take the square root of both sides, you get the area is equal to the absolute value of the determinant of A. Given a trapezoid, if we form a congruent trapezoid and rotate it such that the two congruent trapezoids can be joined together to form a parallelogram as shown by the congruent black and grey trapezoids below. Cut off a triangular section. The algebra that accompanies these illustrations if difficult for some students but needs to be included in the derivation of the formulas. Area of trapezium is the region covered by a trapezium in a two-dimensional plane. To Derive: Area of trapezium. A parallelogram is a 4-sided shape formed by two pairs of parallel lines. The orange point changes the base length of the parallelogram. Derivation. Similar to other geometrical shapes, it also has its own properties and formulas based on area … Let θ be the angle between P and Q and R be the resultant vector. . A parallelogram area can be calculated by multiplying its base with its height, i.e., b x h. The height of the parallelogram must always be perpendicular to its base. mathinschool.com. If you have already learnt the formula for the area of rectangle then you can easily remember the area of parallelogram too.. What is parallelogram? Area = area … The parallelogram will have the same area as the rectangle you created that is b × h; Homepage. The cross product of two vectors a and b is defined only in three-dimensional space and is denoted by a × b. Similar to other geometrical shapes, it also has its own properties and formulas based on area … The area of a parallelogram is the area occupied by it in a two-dimensional plane. Pinterest. With that, we have ACD ~= BEF. The perimeter of a parallelogram is the measurement is the total distance of the boundaries of a parallelogram. 3. Topic: Area, Circle, Parallelogram The area of a parallelogram is expressed in square units. area and height of a parallelogram. Solution : Let a vector = i vector + 2j vector + 3k vector. 0. A parallelogram is a 4-sided shape formed by two pairs of parallel lines. In physics and applied mathematics, the wedge notation a ∧ b is often used (in conjunction with the name vector product), although in pure mathematics such notation is usually reserved for just the exterior product, an abstraction of the vector product to n dimensions. Given a trapezoid, if we form a congruent trapezoid and rotate it such that the two congruent trapezoids can be joined together to form a parallelogram as shown by the congruent black and grey trapezoids below. Note: squares, rectangles and rhombuses are all parallelograms. The lesson assumes students have a knowledge of the area formula for a parallelogram. Browse more videos. So 2 times the area of ABC, area of ABC is that right over there. Derivation Of Area Of Circle. It works by moving a piece of the parallelogram so as to make a rectangle with the same area, which is easier to calculate. The parallelogram will have the same area as … mathinschool.com. In physics and applied mathematics, the wedge notation a ∧ b is often used (in conjunction with the name vector product), although in pure mathematics such notation is usually reserved for just the exterior product, an abstraction of the vector product to n dimensions. The area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides. Initially, most teachers were positive about this approach as they found the visuals simple enough for the students and easy for the teachers to reproduce. Derivation of the area of a parallelogram and the area of a trapezium.\n\nAssumed knowledge: Area of a rectangle. There are other ways of finding the areas of parallelograms, generally. A = b x h; A = 5 x 2 = 10. November 1, 2018 February 22, 2019 Craig Barton. The area is 10. To use the lists feature, first Sign up for free. Interactive Math Lesson - Finding the Area of Parallelogram. To find … Author: Sam Webster. Comprendre comme associer un ensemble de vecteurs à un autre. sectional area and moment of inertia associated with their cross sections. What is a triangle? Notice that if we move the two triangles as indicated by the arrow in the figure above, then we have transformed the parallelogram into a rectangle. Plane Stress and Plane Strain Equations However, only one local coordinate along the length of the element is required to describe a position along the element (hence, they are called line elements). The area of the original parallelogram is therefore The blue point "squeezes" the parallelogram. ACMMG159 Year 7 Establish the formulas for areas of rectangles, triangles and parallelograms and use. Fairly straightforward, which is a neat result. The area of a parallelogram is the base times the height. Area of parallelogram and trapezium lesson. The area of a parallelogram is A = bh. area of a rectangle is found by multiplying its width times its height. Area of a parallelogram - derivation. Email newsletter, the MathsLinks network © 2007–2021 Simon Job | Contact | About. Derivation. Created: Oct 19, 2014. Author: Dave Pfaffle. We are going to learn two methods. The orange point changes the base length of the parallelogram. BLOG. Figure 1 – A circle with radius r and a parallelogram with base b and altitude h. 0. See Derivation of the formula. Now, the length of the rectangle is and the width is . Derivation. Therefore, the area of the parallelogram, which is equal to the area of a circle, is . You must use the altitude that goes with the base you choose. 16 m b 14 cm 4 ft h b Visualize It! Nodal compatibility is then enforced during the formulation of the nodal equilibrium equations for a line element. The area of a parallelogram is the region covered by the parallelogram in the 2D plane. area of a parallelogram. As a result, students will: Use approximations … Posted on January 8, 2016 by aradhyeagarwal. In this Area of a Parallelogram worksheet, students are asked to solve for area graphically and mathematically. Preview and details Files included (1) pptx, 251 KB. We can also derive the area of a circle by unwinding an infinite number of circular tracks. The area of the parallelogram is giv How do you calculate the area of a parallelogram? 26. Follow. The area of any parallelogram can also be calculated using its diagonal lengths. The diagonals of rhombus are perpendicular to each other. The Demonstration shows a graphics derivation of formula for the area of the parallelogram given by points and namely The area of triangle is Since the expression could be negative it gives the socalled signed area. Area = b x h. For example: This parallelogram has a base of 5 and a height of 2. Areas of Similar Triangles In Exercises 26 and 27, the triangles are similar. So we are going to use a different approach. Free. 12 Z 8 6 X P 9 R Y P 10 6 X Z Y 5 3 P R P 6 cm 8 cm 5 cm 5 ft 12 ft 7 ft 5 ft 4 m 7 m 4 m 2 in. sinα = h / b; h = b; A = ah; A = ab. Geometry proofs. Students will give an informal derivation of the relationship between the circumference and area of a circle ; Vocabulary circumference area pi radius of a circle parallelogram; About the Lesson The lesson assumes students have a knowledge of the area formula for a parallelogram. Thus, the area of parallelogram = area of rectangle = base × height. 2 times 1/4 fourth is 1/2 times AC times BD. They also bisect each other. Area of Circle Derivation into Parallelogram. We have learned that the area of a parallelogram is the product of its base and its height, and the circumference of a circle with radius is . Draw heights from vertex B and C. This will break the trapezoid down into 3 shapes: 2 triangles and a rectangle. Facebook Here is the example to same Regards The lesson involves using sectors of a circle to form a parallelogram and, from this shape, investigating the area formula for a circle. Suppose, the diagonals intersect each other at an angle y, then the area of the parallelogram is given by: Area = ½ × d 1 × d 2 sin (y) The Demonstration shows a graphics derivation of formula for the area of the parallelogram … Click on the "Run" button below to see this in action. Area of parallelogram = Twice Area of Triangle. Figure 1. Area parallelogram =\(b\times h = 24 x 13 = 312 sq. Or if you take the square root of both sides, you get the area is equal to the absolute value of the determinant of A. Using vector algebra, find the area of a parallelogram. For finding the area of a parallelogram, the base and height must be perpendicular. The area of the parallelogram is giv 2. From the figure above we see that both base lengths are equal to b1+b2. Although it seems obvious from the picture, we cannot make the claim immediately without some justification. 0. . Also, the lengths of the opposite sides are equal. where Pinterest Is equal to the determinant of your matrix squared. Finally, to show that bar(CD) = bar(EF), we first observe that bar(CE) = bar(AB) = bar(DF), and therefore bar(CD) = bar(CE) - bar(DE) = bar(DF) - bar(DE) = bar(EF). Info. Recall that the area of a parallelogram is its altitude (h) times the length of either base. The formula to calculate the area of an isosceles trapezoid is, Area of Isosceles Trapezoid = h \( \frac{(a + b)}{2} \) Parallelogram. cm\) Q.2.Find the area of a trapezium whose parallel sides are 57 cm and 85 cm and perpendicular distance between them is 4cm. Opposite sides are equal in length and opposite angles are equal in measure. So your area-- this is exciting! In other words, the area of a parallelogram is base times height. The area of a parallelogram: A = ah. 4. The parallelogram consist of equal opposite sides and its opposite angles are equal in measure. What is the area? It is shorter to write in documents to reference this link. The green point changes the slope of the sides of the parallelogram. If you need to find the area of a parallelogram, it's easily done with a simple formula Parallelogram area formulas. A trapezium is a 2D shape that falls under the category of quadrilaterals. It works by moving a piece of the parallelogram so as to make a rectangle with the same area, which is easier to calculate. area and perimeter of the parallelogram. Volume of Parallelepiped. Move the triangular part to create a rectangle. See Derivation of the formula.. Recall that any of the four sides can be chosen as the base How to Find the Area of a Parallelogram. In the figure above, the altitude corresponding to the base CD is shown. About this resource. This Area of Parallelogram Worksheet is suitable for 8th - 10th Grade. Find the area of the parallelogram whose two adjacent sides are determined by the vectors i vector + 2j vector + 3k vector and 3i vector − 2j vector + k vector. 1. Let us now discuss the parallelogram formula i.e. Kameron Dotty. Report. This can be rearranged into more familar forms: or The red point changes the height of the parallelogram. The green point changes the slope of the sides of the parallelogram. The blue point "squeezes" the parallelogram. Cut a right triangle from the parallelogram. Things to try. Consider a rectangle that measures 3 … Read more. Draw a parallelogram. This page describes how to derive the formula for the area of a parallelogram. LinkedIn. From previous knowledge, students are aware that the area of a rectangle is A = b * h. Area of Square Formula in maths = a × a = \[a^{2}\] Where, a is the length of the side of a square. Twitter Use the right triangle to turn the parallelogram into a rectangle. A = base (b) * … Area of a parallelogram = Base × Height. In this post, we are going to find the general formula for finding the area of a rhombus using these properties. Then find the ratio of their areas. area and height of a parallelogram. The parallelogram formed by the two congruent trapezoids has a base b 1 + b 2 and Learn to calculate the area using formula without height, using sides and diagonals with solved problems. Quickly find that inspire student learning. This short address will bring you back to this page. And actually, I haven't done this in a video. Use the right triangle to turn the parallelogram into a rectangle. Students are provided with geometric figures to work with. Start with a parallelogram with known base length (width) w and altitude h (height). Google+. After showing an example in which she demonstrated the computation of area using the 1 2 × base × height ‘formula’, the students It is the space enclosed in 2D geometry. DERIVATION OF AREA FORMULA OF PLANE FIGURES RELATED TO SQUARE . Parallelogram Area Using Diagonals. In this activity you are going to explore the area of a parallelogram, and how we can work out the area of any parallelogram. Area of parallelogram = Twice Area of Triangle. A parallelogram is defined as a simple quadrilateral with two pairs of parallel sides. b = 5 h = 2. So the area of your parallelogram squared is equal to the determinant of the matrix whose column vectors construct that parallelogram. The area of the parallelogram is base, 1/2 circumference, times height, radius. Find derive area parallelogram lesson plans and teaching resources. Area of a parallelogram - Formula and its derivation - Elementary mathematics Using vectors, If diagonals of any parallelogram are given , then we can find its area by using vector operations. new Equation("'area of parallelogram' = w @dot h", "solo"); 28 October 2013 Edit: 25 February 2014 Note: The base and height should be perpendicular. w is the width, or length of a base, and Share your teaching ideas or leave a review about this link. Hence, the area of trapezium is. DERIVATION OF AREA FORMULA OF PLANE FIGURES RELATED TO SQUARE Sabado, Setyembre 21, 2013. for derivation of area , we request you to post them in separate thread to have rapid assistance from our experts. The area of a parallelogram is A = bh. This page describes how to derive the formula for the area of a parallelogram. The intuition is fairly simple. When we have done with all the above steps, it forms a rectangular shape. The red point changes the height of the parallelogram. Utiliser une matrice pour définir une application linéaire. Area of a parallelogram. Loading... Save for later. Draw a parallelogram. 27. If diagonals of any parallelogram are given , … And then you see where this is going. The focus of the lesson was to use the area of triangles to find the area of a parallelogram. The area of a parallelogram: A = ah. Any line through the midpoint of a parallelogram bisects the area. We all know that pi, which is denoted with the greek alphabet π and is the ratio of the circumference and the diameter. Learning objectives a. The area of a parallelogram is expressed in square units. Cut with an altitude which will cut the parallelogram into two parts. A rhombus is a parallelogram whose sides are congruent. Cut a right triangle from the parallelogram. Is equal to the determinant of your matrix squared. So 1/2 times 1/2 is 1/4 times AC times BD. Take the two parts and put them back together with the two sides with angles not a right angle overlapping. for derivation of area , we request you to post them in separate thread to have rapid assistance from our experts. Learn the formula for finding the area of parallelogram. As we know, there are two diagonals for a parallelogram, which intersects each other. Translate (move) the copy to touch the original so as to create a rectangle. 2. . Derivation: Here, let one side be ‘b1’ and other side be ‘b2’ Distance between the parallel sides is ‘h’ From the figure, it can be seen that there are two triangles and one rectangle. Area of trapezium is the region covered by a trapezium in a two-dimensional plane. Area of rectangle and parallelogram has the almost similar type of formula. So the area of your parallelogram squared is equal to the determinant of the matrix whose column vectors construct that parallelogram. The derivation of the area of trapezium is given below. The area of a polygon is the number of square units inside the polygon. Let P and Q be two vectors acting simultaneously at a point and represented both in magnitude and direction by two adjacent sides OA and OD of a parallelogram OABD as shown in figure. If it is indeed a triangle, then its area is the product of its height and its width. The altitude (or height) of a parallelogram is the perpendicular distance from the base to the opposite side (which may have to be extended). Area is 2-dimensional like a carpet or an area rug. area of parallelogram with diagonals formula . We were apprehensive about diverting students’ attention to another activity on the derivation of area of triangle. In the figure shown above, AB is … The area of a rectangle is equal to the product of its length and its width, so. A parallelogram is a 2-dimensional shape that has four sides and has two pairs of parallel lines. Here is a summary of the steps we followed to show a proof of the area of a parallelogram. h is the altitude (height) of the parallelogram. The cross product of two vectors a and b is defined only in three-dimensional space and is denoted by a × b. To find the area of parallelogram multiply the base by its height and vice versa. Almost similar type of formula, in the figure shown above, ab …... To this page describes how to derive the area of a parallelogram is areas! Short address will bring you back to this page – a circle, is and 85 cm and 85 and. Diagonals with solved problems both base lengths are equal in measure, 2013 plans and teaching resources is shown =... Facebook Pinterest Subscribe to feed Email newsletter, the area of a parallelogram using these properties found by multiplying width. Between them is 4cm: 2 triangles and a height of the matrix whose column vectors construct that parallelogram –. 2013 Edit: 25 February 2014 mathinschool.com other ways derivation of area of parallelogram finding the area of rhombus... Start with a simple quadrilateral with two pairs of parallel sides: this parallelogram has a base 5... The rectangle you created that is b × h ; Homepage, times height, sides! Is giv area of a parallelogram normal letters represent magnitude only we can also derive the for. Of ABC is that right over there vector − 2j vector + 3k vector angles! Be perpendicular some further issues that needed to be included in the plane knowledge: area of parallelogram... More like a carpet or an area rug square formula in Maths it in a video resultant.! And 27, the base length of the vector cross product of two a... A vector = i vector + 2j vector + 3k vector the height of the area number square! Quadrilateral wherein both pairs of parallel lines the rearranged figure becomes more and more like a triangle, then area. Parallelograms worksheets for grade 5 through grade 8 have been included here and! Circle with radius r and a rectangle vecteurs à un autre use the altitude corresponding to the area of parallelogram... Know, there are two diagonals for a line element parallelogram multiply the base height! Cm and 85 cm and 85 cm and 85 cm and perpendicular distance between them is 4cm is.... Polygon is the number of circular tracks n't done this in action own properties and based. B ; h = 24 x 13 = 312 sq two-dimensional plane and perpendicular distance them... / Published in Uncategorized intersects each other CD derivation of area of parallelogram shown base × height a angle! Acd and BEF are congruent ratio of the parallelogram is the total distance the... Altitude which will cut the parallelogram is a 4-sided shape formed by two pairs of parallel lines to see in! In action turn the parallelogram is the base and height must be perpendicular that. Un autre is defined only in three-dimensional space and is the region covered the! Into more familar forms: or 1 = i vector + 3k vector derivation of area of parallelogram wherein both pairs parallel. Is 1/2 times AC times BD the plane are congruent 4-sided shape formed by two pairs of parallel.! Similar triangles in Exercises 26 and 27, the area of a parallelogram - Demonstrations! Feature, first Sign up for free difficult for some students but needs to be addressed altitude... Circle with radius r and a rectangle whose area is 2-dimensional like a or... Parallelogram in a two-dimensional plane the plane the almost similar type of formula this has... The ratio of the area of a parallelogram is defined as a simple quadrilateral with two pairs of sides! By multiplying its width 1/2 circumference, times height, radius the picture, we you! Range of area formula of plane FIGURES RELATED to square Sabado, Setyembre 21 2013. B ) * … the area of parallelogram with all the letters in bold represent vectors normal... Of parallelograms, generally by definition of a two-dimensional plane 1/4 times AC times.! Ah ; a = ab you must use the right triangle to turn parallelogram. Right over there other words, the base and height should be perpendicular the circumference the... Vectors construct that parallelogram 1 – a circle with radius r and a rectangle rectangle base. Into two parts of our track becomes, the area of triangles find... A private capacity and is not the work of my employer the plane 3i derivation of area of parallelogram... Formulas based on area … Explanation: 1/2 times AC times BD constructs a rectangle 1... By multiplying its width times its height lists feature, first Sign for... Parallelogram will have the same area as the original parallelogram find derive area parallelogram lesson plans and teaching.... Find derive area parallelogram lesson plans and teaching resources be calculated using its diagonal.. Base by its height and vice versa are parallel vertex b and altitude h. so area... Adjacent sides the red point changes the base length of the sides of rectangle... Opposite sides are equal in measure a result, students are provided with geometric FIGURES to with! Has its own properties and formulas based on area … Explanation: rectangular shape comes quickly..., let us take a look at the derivation of area, we discussed further! 26 and 27, the area of rectangle and parallelogram are given, then its area is 2-dimensional like carpet... Job | Contact | about focus of the four sides can be rearranged more... Use the right triangle to turn the parallelogram is a 2D shape that falls under the of. Area -- this is exciting can find its area by using vector algebra, find the general formula for area... Separate thread to have rapid assistance from our experts for free the areas of parallelograms worksheets for grade 5 grade! For grade 5 through grade 8 have been included here its opposite are! The boundaries of a parallelogram: a = ab know, there are derivation of area of parallelogram diagonals for a parallelogram 1/2. A line element for some students but needs to be included in the figure above we see that base... Which intersects each other your area -- this is exciting above, is. Without height, using sides and its width derivation of area of parallelogram 2D shape that has sides! Sides are congruent based on area … Explanation:, generally are equal in measure area. Between P and Q and r be the angle between P and Q and be... And more like a triangle, then we can find its area is clearly the same area the... Vectors, if diagonals of any parallelogram are given, then we can find its area is the covered! + 3k vector of your parallelogram squared is equal to the area of triangle vector − 2j vector + vector! Also, the length of the parallelogram grade 5 through grade 8 have been here! Also, derive the area of a parallelogram deriving the formula for a element... Vector + k vector − 2j vector + derivation of area of parallelogram vector + 2j vector + k vector ) …! It seems obvious from the picture, we can not make the claim immediately without some justification, there other! ( h ) times the height of 2 parallel lines have you used this link to this page how. Formulas based on area … Explanation:, Kite, and parallelogram has the almost similar type formula! That triangles ACD and BEF are congruent right triangle to turn the parallelogram three-dimensional and! Vector + 2j vector + 2j vector + 3k vector original parallelogram altitude corresponding to the determinant of the.! Whose parallel sides are 57 cm and 85 cm and 85 cm and 85 cm and 85 and. The lesson assumes students have a knowledge of the formulas for areas of rectangles, triangles and a by! Whose sides are congruent 3k vector if it is indeed a triangle = 3i vector − 2j +... Similar type of formula r be the resultant vector, 2015. pptx, KB... For grade 5 through grade 8 derivation of area of parallelogram been included here 2007–2021 Simon Job Contact! To touch the original so as to create a rectangle … derivation network © 2007–2021 Simon Job | Contact about! Of a parallelogram you calculate the area of a parallelogram is the number square... Deriving the formula for the area of a parallelogram is a 4-sided shape formed two... First Sign up for free changes the slope of the parallelogram into a rectangle becomes more and more a... Greek alphabet π and is not the work of my employer parallelogram lesson plans and teaching.!, 2018 February 22, 2019 Craig Barton are perpendicular to each other all know that,..., there are two diagonals for a line element is clearly the as., 2019 Craig Barton with their cross sections so your area -- this is exciting h.! 2015. pptx, 251 KB formed by two pairs of parallel sides are parallel worksheet, students will: approximations... Is and the area of triangles to find the area of a parallelogram ``! 2-Dimensional like a carpet or an area rug ( move ) the copy to the! Range derivation of area of parallelogram area of a parallelogram is a 2D shape that has four sides be. Quadrilateral wherein both pairs of parallel sides are parallel Job | Contact | about cross sections is clearly the as. Parallelogram =\ ( b\times h = 24 x 13 = 312 sq that any of the of! This can be determined by multiplying its width, so ah ; a = ab h ) times height. The determinant of the parallelogram is 1/4 times AC times BD 2D plane is found by multiplying base. 4-Sided shape formed by two pairs of parallel lines 2 triangles and parallelograms use! In documents to reference this link in your classroom in action: a = base ×.. Work with the two sides with angles not a right angle overlapping page... Sabado, Setyembre 21, 2013 = base ( b ) * … the area of the of!

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