Question

If an isosceles triangle has a perimeter of 22 cm and base 10 cm, then find its area.

Answer 1

Let each of its equal sides be x.
Then, 2x + 10 = 22 $\Rightarrow$ x = 6 cm
Hence, the sides are 6 cm, 6 cm and 10 cm.
Using the Heron's formula,
Area (A)=$\sqrt{s(s-a)(s-b)(s-c)}$
where s = semi- perimeter and a,b,c are the three sides of the triangle.
Semi-Perimeter (s) =$\frac{1}{2}\times Perimeter$
$=\frac{1}{2}\times 22=11cmArea\left(A\right)=\sqrt{11(11-6)(11-6)(11-10)}=\sqrt{11\left(5\right)\left(5\right)\left(1\right)}=5\sqrt{11}c{m}^{2}Area=5\sqrt{11}c{m}^2$