Question

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

Answer 1

Refer to the attached image..

hope it helps you:-)

Answer 2

Answer:

Given :

A trapezium such that whose parallel sides are 25 m and 10 m. And non parallel sides are 14 m and 13 m.

Find :

Area of the field (trapezium).

Construction :

Draw a perpendicular from B on CE.

Assume :

Let ABCD a trapezium such that AD = 14 m, CD = AB = CD = 10 m, DE = 25 mand BE = 13 m respectively.

Solution :

CE = DE - DC

CE = 25 - 10 = 15 m

Semi-perimeter of ΔBCE = Sum of sides/2

s = (a + b + c)/2

Here.. a = BC, b = CE and c = EB

s = (BC + CE + EB)/2

s = (14 + 15 + 13)/2

s = 42/2

s = 21 m

From Heron's formula

$Area of ΔBEC = \sqrt{s(s - a)(s - b)(s - c)} </p><p>$

$= \sqrt{21(7)(6)(8)}$

= 84 m² _____ (eq 1)

Area of ΔBCE

= 84 = 1/2 × b × h

= 84 = 1/2 × 15 × h

= 84 × 2 = 15h

= h = 11.2 m

(h = BF)

Area of parallelogram ABCD = b × h

=> 10 × 11.2

=> 112 m² ____ (eq 2)

Area of trapezium AEBD = (eq 1) + (eq 2)

=> 84 + 112

=> 196 m²

∴ Area of trapezium is 196 m².