The parallel sides of a trapezium are 25 cm and 15 cm long. Its non-parallel sides are both equal, each being 10 cm long. Find the area of the trapezium.
Given:
The parallel sides of a trapezium are 25 cm and 15 cm long. Its non-parallel sides are both equal, each being 10 cm long.
To do:
We have to find the area of the trapezium.
Solution:
Height of the trapeziumis AE.
In triangle ADE,
$AD^2=AE^2+DE^2$
$10^2=AE^2+5^2$
$100=AE^2+25$
$AE^2=100-25=75$
$AE=\sqrt{75}=5\sqrt3$
We know that,
Area of a trapezium of height h and non-parallel sides a and b$=\frac{1}{2}\times h(a+b)$
$=\frac{1}{2}\times 5\sqrt3(25+15)$
$=\frac{1}{2}\times 5\sqrt3(40)$
$=100\sqrt3$
The area of the trapezium is $100\sqrt3$.
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