An isosceles triangle has perimeter 40 cm; the equal sides are 15 cm each. Find the area of the triangle.

Perimeter = 40 cm

Equal sides = 15 cm each

$$\text{Base} = 40 - 15 - 15 = 10 \text{ cm}$$

Height from apex to base:

$$h^2 + 5^2 = 15^2$$

$$h^2 = 225 - 25 = 200$$

$$h = \sqrt{200} = 10\sqrt{2} \text{ cm}$$

$$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$

$$= \frac{1}{2} \times 10 \times 10\sqrt{2}$$

$$= 50\sqrt{2} = 70.71 \text{ cm}^2$$