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(b1 + b2)
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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