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.

Question

Philoid · Accepted Answer

Let ABCD be the given trapezium whose

parallel sides are:

AB = 25m and CD = 10m

And,

Non-parallel sides are AD = 13m and BC = 14m

Now,

CM perpendicular to AB and CE ‖ AD

In

BC = 14m, CE = AD = 13m and

BE = AB – AE

= 25- 10

= 15m

Semi perimeter of =

=

= 21cm

Now,

Using Heron’s formula,

Area of =

=

= 84m²

1/2 *15 *CM = 84

CM = m²

Area of parallelogram AECD = Base *Altitude

= AE *CM

= = 112m²

Area of trapezium ABCD = Area of AECD + Area of triangle BCE

= (112 + 84) m²

= 196m²