Question

Draw a quadrilateral ABCD of which AB = 4 cm, BC =5 cm, CD = 4.8 cm, DA = 4.2 cm and Diagonal AC =6 cm. Draw a triangle with equal area of that quadrilateral.​

Answer 1

A. Draw the given quadrilateral ABCD.

B. Draw the diagonal AC of quadrilateral ABCD.

C. Draw a parallel line through point D to diagonal AC of quadrilateral ABCD which intersects at F produced BC.

D. DF||AC, ABF is the required triangle.

Proof:

∆ADC = ∆ACF (on same base AC and between same parallels AC and DF)

∴ ∆ ADC = ∆ ACF

∆ABC + ∆ADC = ∆ACF + ∆ABC (adding area of ∆ABC on both sides)

∴ quadrilateral ABCD = ∆ABF