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ML Aggarwal Solutions Class 8 Mathematics Solutions for Mensuration Exercise 18.1 in Chapter 18 - Mensuration
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The perimeter of a trapezium is 52 cm. If its non-parallel sides are 10 cm each and its altitude is 8 cm, find the area of the trapezium.
Answer:
Given,
Perimeter of a trapezium = 52 cm
Length of each non-parallel side = 10 cm
Altitude DL = 8 cm
Now,
In right ∆DAL, by Pythagoras Theorem we have
DA2 = DL2 + AL2
(10)2 = (8)2 + AL2
100 = 64 + AL2
AL2 = 100 – 64 = 36 = (6)2
∴ AL = 6 cm
Similarly,
BM = 6 cm and DC = LM
Also, we have
Perimeter = AB + BC + CD + DA
and CD = DA
So, CD + DA = 2DA
But,
AB + CD = Perimeter – 2 AD
= 52 – 2 × 10
= 52 – 20
= 32 cm
Thus, the area of trapezium = ½ × (sum of parallel sides) × altitude
= ½ × 32 × 8
= 128 cm2
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