Question

A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.

Answer 1

In the figure ABCD is the field. Draw CF || DA and CG ⊥ AB. 

DC = AF = 10 m, AD = FC = 13 m 

For ∆BCF, a = 15 m, b = 14 m, c = 13 m 

∴ s = a + b +  c / 2 = 15 +14 +13 / 2 m = 21 m

Also, area of ∆BCF = 1/ 2 × base × height 

= 1/ 2 × BF × CG 

⇒ 84 = 1/ 2 × 15 × CG 

⇒ CG = 84 x 2/ 15 m = 11.2 m 

∴ Area of the trapezium = 1/ 2 × sum of the parallel sides × distance between them. = 1/ 2 × (25 + 10) × 11.2 m² 

= 196 m² 

Hence, area of the field = 196 m² Ans.