Question

Area of an isosceles triangle, one of whose equal side is 5 units and base 6 units is __________.

Answer 1

Given:
Base of isosceles triangle is 6 units.
equal sides of isosceles triangle is 5 units.


Now, using Heron's formula:
If a, b and c are three sides of a triangle, then
area of the triangle = $\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$ , where $s=\frac{a+b+c}{2}$.


Here, $s=\frac{6+5+5}{2}=\frac{16}{2}=8$

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{triangle}=\sqrt{8\left(8-5\right)\left(8-5\right)\left(8-6\right)} \\ =\sqrt{8\left(3\right)\left(3\right)\left(2\right)} \\ =\sqrt{\left(2\times 2\times 2\right)\left(3\right)\left(3\right)\left(2\right)} \\ =\left(3\times 2\times 2\right) \\ =12{\mathrm{cm}}^2 \end{gathered}$$


Hence, the area of the triangle is $\underline{12{\mathrm{cm}}^2}$.