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

Area of the field = 196 sq. m.

Step-by-step explanation:

Area of Trapezium = Area of Rectangle + Area of Triangle

Please refer to the attached picture for the diagram.

Heron's formula for area of triangle = root of [ s (s-a) (s-b) (s-c) ] where s = half of perimeter of the triangle.

Area of Triangle with sides 13m, 14m and 15m:

s = 13 + 14 + 15 / 2 = 21 m

Area of triangle = root of [ 21 (21 - 13) (21 - 14) (21 - 15)] = root of (21 * 8 * 7 * 6) = 84 sq. m.

Area of a triangle with base 15 = 1/2 * 15 * height = 84

So height = 56 /5 m

Area of rectangle = length * breadth = 10 * 56 / 5 = 112 sq. m

So area of trapezium = 84 + 112 = 196 sq. m.