Question

A Field is in Shape of trapezium with parallel sides25m and10 m. and non parallel sides are 14m and 13m. find the area of the field.

Answer 1

We have,
Parallel sides of 25m and 10m.
Non-parallel sides of 14m and 13m.

Let us consider a trapezium PQRS where PQ and RS are the parallel sides.
Let us draw QV parallel to PS and QT perpendicular on SR.

Now, PQVS is a parallelogram where QV = 14 m, SV = 10 m
Thus, VR = SR - SV = 25 - 10 = 15 m.

Now, we have a triangle QRV.

Area of the triangle by using Heron's formula,

Semi-perimeter, s = (13 + 14 + 15)/2
= 21 m
By, Heron's law,

ar(QRV) = √{s (s-a)(s-b)(s-c)}
= √21 (21-13)(21-14)(21-15)
= √21 × 8 × 7 × 6
= √7056
= 84 m²

Now,
ar(QRV) = 1/2 × RV × QT
⇒ 84 = 1/2 × 15 × QT
⇒ 168 = 15 QT
⇒ 11.2 m = QT

Height of the trapezium = 11.2 m

Now,

Area of trapezium, ar(PQRS) = 1/2(a+b)h

= 1/2 ( 25 + 10) 11.2
= 1/2 × 35 × 11.2
= 196 m²

Hence, the area of the given trapezium is 196m².

Answer 2

hey here is your answer

area of trapezium are = "196m2"

I think my answer is capable to clear your confusion..