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.

# 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.

Register to Get Free Mock Test and Study Material

+91

Live ClassesRecorded ClassesTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

We know that, Heron's formula

Area of triangle =

where, s is the semi-perimeter = half of the perimeter

and  a, b and c are the sides of the triangle

DC = AF = 10 m, DA = CF = 13 m

So, FB = 25 - 10 = 15 m

In ∆CFB, a = 15 m, b = 14 m, c = 13 m.

Semi Perimeter = s = (a $+$ b $+$ c)/2

= (15 $+$ 14 $+$ 13)/2

= 42/2

s = 21 m

By using above formula,

Area of ∆CFB =

= 84 m2

and

Area of ∆CFB = 1/2 $×$ base $×$ height

84 = 1/2 $×$ BF $×$ CG

84 = 1/2$×$ 15 $×$ CG

CG = (84 $×$2)/15

CG = 11.2 m

Area of trapezium ABCD = 1/2 $×$ sum of parallel sides$×$ distance

= 1/2 $×$ (AB $+$ DC) $×$ CG

= 1/2 $×$ (25 $+$ 10) $×$ 11.2

= 196 m2

Hence the area of the field is 196 m2.

## Related content

 Distance Formula Perimeter of Rectangle Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formulae Volume of Cylinder Perimeter of Triangle Formula Area Formulae Volume Formulae  