Question

The lateral surface area of a square pyramid comprises of equilateral triangles and the length of the lateral edge is $50cm$. What is its lateral surface area?

• A. $2500(1+\sqrt{3})$
• B. $2500(2+\sqrt{3})$
• C. 2500
• D. $2500\sqrt{3}$

Answer 1

The correct option is D

$2500\sqrt{3}$

Given that the triangular face of the pyramid is equilateral and the length of the base edge is $50cm$.
The lateral surface area of the square pyramid comprises four equilateral triangles of side $50cm$ each.

Area of an equilateral triangle of side $acm$ = $\frac{\sqrt{3}}{4}{a}^2$

Thus, in this case we have Area of the triangle = $\frac{\sqrt{3}}{4}(50{)}^2=625\sqrt{3}$
$⟹$ Area of four such equilateral traingles = Lateral surface area of the pyramid

$⟹$ Area of four such equilateral traingles $=4\times 625\sqrt{3}=2500\sqrt{3}$