The length of each of the two equal sides of an isosceles triangle is 41 cm and the length of its base is 18 cm. The area (in cm²) of the triangle is:​

Correct option is C

Given:

Length of equal sides = 41 cm

Length of base = 18 cm

Concept Used:

In an isosceles triangle, the altitude from the vertex to the base bisects the base, forming two right-angled triangles.

Formula Used:

Height h = $$\sqrt{a^2 - \left(\frac{b}{2}\right)^2}$$​​

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

Solution:

Base b = 18 $$\Rightarrow \frac{b}{2}$$​ = 9

Equal side a = 41

​$$h = \sqrt{41^2 - 9^2} = \sqrt{1681 - 81} = \sqrt{1600} = 40 \text{ cm}$$​​

Now,

Area = $$\frac{1}{2} \times 18 \times 40 = 9 \times 40 = 360 \text{ cm}^2$$​​