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Question

If an isosceles triangle has a perimeter of 20 cm and base 4 cm, then its area is ___ .

A
215 cm2
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B
415 cm2
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C
215 cm2
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D
43 cm2
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Solution

The correct option is B 415 cm2
Let each of its equal sides be x.
Then, 2x+4=20 x=8cm
Hence, the sides are 8 cm, 8 cm and 4 cm.
Using the Heron's formula,
Area(A)=s(sa)(sb)(sc)
where s = semi- perimeter and a,b,c are the three sides of the triangle.
SemiPerimeter(s)=perimeter2
=202 =10 cm
A=10 (108)(108)(104)
=10×2×2×6
=415 cm2

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