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Question

The base of an isosceles triangle is 12 cm and its perimeter is 32 cm. Find its area.

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Solution

Let each of the equal sides be a cm.
a + a + 12 = 32 ⇒ 2a = 20 ⇒ a = 10
∴ b = 12 cm and a = 10 cm
Area of the triangle = 12×b×a2-b24 sq. units
= 12×12×100-1444 cm2 = 6-100-36 cm2
= 6×64 cm2 = (6 × 8) cm2
= 48 cm2

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