# The area of a trapezium with equal non-parallel sides is 168 m². If the lengths of the parallel sides are 36 m and 20 m, find the length of the non-parallel sides.

**Solution:**

__Area of Trapezium__(A) = 1/2 × (sum of parallel sides) × height

A = 1/2 × (36 + 20) 1/2 × height(h)

A = 168m²

168 = 1/2 × 56 × h

h = (168 × 2)/56 = 6m

The area of the rectangle formed in the diagram above = 20 × 6 = 120m ²

The Area of the two triangles = 168 - 120 = 48m²

The area of the two triangles = 1/2 × DE × 6 + 1/2 × FC × 6 = 3(b_{1} + b_{2})

3(DE + FC) = 48

DE + FC = 48/3 = 16

Since AD = BC (given)

DE = FC

Therefore

DE = FC = 16/2 = 8

Applying the __pythagorean theorem__ to any of the two equal triangles AED and BFC we get

(Non Parallel Side)² = 8² + 6² = 64 + 36 = 100

Non Parallel Side = √100 = 10

**✦ Try This: **The area of a trapezium with equal non-parallel sides is 432 m². If the lengths of

the parallel sides are 52 m and 20 m, find the length of the non-parallel sides.

Area of Trapezium(A) = 1/2 × (sum of parallel sides) × height

A = 1/2 × (52 + 20) 1/2 × height(h)

A = 432m²

432 = 1/2 × 72 × h

h = (432 × 2)/72 = 12m

The area of the rectangle formed in the diagram above = 20 × 12 = 240m ²

The Area of the two triangles = 432 - 240 = 192 m²

The area of the two triangles = 1/2 × DE × 12 + 1/2 × FC × 12 = 6(DE + FC)

6(DE + FC) = 192

DE + FC = 192/6

DE + FC = 32

Since AD = BC (given)

DE = FC

Therefore

DE = FC = 32/2 = 16

Applying the pythagorean theorem to any of the two equal triangles AED and BFC we get

(Non Parallel Side)² = 12² + 16² = 144 + 256 = 400

Non Parallel Side = Ad = BC = √400 = 20m

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 11

**NCERT Exemplar Class 8 Maths Chapter 11 Problem 67**

## The area of a trapezium with equal non-parallel sides is 168 m². If the lengths of the parallel sides are 36 m and 20 m, find the length of the non-parallel sides.

**Summary:**

The area of a trapezium with equal non-parallel sides is 168 m². If the lengths of the parallel sides are 36 m and 20 m, the length of the non-parallel sides is 10m

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