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📐 Mathematics - Class 10
Lesson 11 · Construction of a Triangle and a Quadrilateral Equal in Area

Construction of triangles and parallelograms equal in area

MathematicsSubject
8 minEstimated read
Activity 3

Parallelogram equal in area to a triangle

Method
  • Draw a rough sketch of a triangle ABC and place the values.
  • Construct a \( \triangle ABC \) in which AB = 4 cm, BC = 6.5 cm and \( \angle ABC = 120^\circ \).
  • Draw ST parallel to BC through A, making \( \angle BAS = \angle ABC \).
  • Bisect BC and mark the midpoint D. Take an arc of radius 5 cm from the point B on the line ST, cutting it at a point, and name it P.
  • Take an arc of radius BP from the point D on the line PT, cutting it at a point, and name it Q. Join D and Q.
Discussion
  • The area of the parallelogram PBDQ is equal to the area of \( \triangle ABC \). How? Discuss with your friend.
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