Question

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

Answer 1

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 = $\left\{\frac{1}{2}\times b\times \sqrt{a^2-\frac{b^2}{4}}\right\}$ sq. units
= $\left\{\frac{1}{2}\times 12\times \sqrt{100-\frac{144}{4}}\right\}$ cm² = $\left(6-\sqrt{100-36}\right)$ cm²
= $\left(6\times \sqrt{64}\right)$ cm² = (6 $\times$ 8) cm²
= 48 cm²