Question

The base of an isosceles triangle is 48 cm and one of its equal sides is 30 cm. Find the area of the triangle.

Answer 1

Let each of the equal sides be a cm.
b = 48 cm
a = 30 cm
Area of the triangle = $\left\{\frac{1}{2}\times b\times \sqrt{a^2-\frac{b^2}{4}}\right\}$ sq. units
= $\left\{\frac{1}{2}\times 48\times \sqrt{{\left(30\right)}^2-\frac{{\left(48\right)}^2}{4}}\right\}$ cm² = $\left(24\times \sqrt{900-\frac{2304}{4}}\right)$ cm²
= $\left(24\times \sqrt{900-576}\right)$ cm² = $\left(24\times \sqrt{324}\right)$ cm² = (24 $\times$ 18) cm² = 432 cm²
∴ Area of the triangle = 432 cm²