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The parallel side of a trapezium are 40 and 70 cm. If the non parallel side are equal, each being 25 cm, find the area of the trapezium
Given:
The parallel sides of a trapezium are 40 cm and 70 cm long. Its non-parallel sides are both equal, each being 25 cm long.
To do:
We have to find the area of the trapezium.
Solution:
Height of the trapezium is AE.
In triangle ADE,
$AD^2=AE^2+DE^2$
$25^2=AE^2+15^2$
$625=AE^2+225$
$AE^2=625-225=400$
$AE=\sqrt{400}=20$
We know that,
Area of a trapezium of height h and non-parallel sides a and b$=\frac{1}{2}\times h(a+b)$
$=\frac{1}{2}\times 20 \times (40+70)$
$=10\times(110)$
$=1100\ cm^2$
The area of the trapezium is $1100\ cm^2$.
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