Question

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

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

Answer 1

The correct option is B

$2500(1+\sqrt{3})$

Given that the length of the base edge is $50cm$.
Thus, the area of the base = $50\times 50=2500c{m}^2$

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 = $\frac{\sqrt{3}}{4}(50{)}^2=625\sqrt{3}$

$⟹Areaoffoursuchequilateraltraingles=4\times 625\sqrt{3}=2500\sqrt{3}$

$⟹Surfaceareaofthesquarepyramid=2500+2500\sqrt{3}=2500(1+\sqrt{3})$