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

ABCD is a trapezium. AB || DC. 

Draw AE || BC and AF ⊥ DC. 

∴ ABCE is a parallelogram. 

DE = DC – EC = 25 – 10 

DE = 15 cm. 

Sides of ∆ADE a = 14 cm, 

b = 13 cm. c = 15 cm. 

∴ Perimeter= a + b + c 

= 14 + 13 + 15 = 42 cm.

Area of quadrilateral 

ABCE = base × height 

= EC × AF 

= 10 × 11.2 

= 112.0 = 112 sq.cm. 

∴ Complete area of trapezium ABCD, A 

A = Area of ∆ADE + Area of quadrilateral ABCE 

= 84 + 112 

= 196 sq.cm.