Find the area of an isosceles triangle with perimeter 36 cm and base 16 cm.

Given:

Perimeter = 36 cm

Base = 16 cm

Let a be the length of the equal sides of the triangle.

Perimeter = 2 x Equal side + Base

⇒ 36 = 2a + 16

⇒ 2a = 36 - 16

⇒ 2a = 20

⇒ a = $\dfrac{20}{2}$

⇒ a = 10 cm

Thus, the triangle has two equal sides, each 10 cm long, and a base of 16 cm.

a = 10 cm, b = 10 cm and c = 16 cm.

The semi-perimeter is:

$∵ s = \dfrac{a + b + c}{2}\\[1em] = \dfrac{10 + 10 + 16}{2}\\[1em] = \dfrac{36}{2}\\[1em] = 18$

∵ Area of triangle = $\sqrt{s(s - a)(s - b)(s - c)}$

= $\sqrt{18(18 - 10)(18 - 10)(18 - 16)}$ cm²

= $\sqrt{18 \times 8 \times 8 \times 2}$ cm²

= $\sqrt{2,304}$ cm²

= 48 cm²

Hence, the area is 48 cm².