Question

All edges of a square pyramid are of equal lengths. If the length of the base edge is $20cm$, what is the lateral surface area?

• A. $400\sqrt{3}$
• B. $100\sqrt{3}$
• C. $300\sqrt{3}$
• D. $200\sqrt{3}$

Answer 1

The correct option is A

$400\sqrt{3}$

The lateral surface area of a square pyramid = $4\times Areaofatriangularfaceofthepyramid$
$\Rightarrow$ L.S.A of a square pyramid = $4\times \frac{1}{2}\times Baseedgeofthetriangle\times Slantheightofthepyramid$
Given that Length of the base edge= Length of the lateral edge= $20cm$.
Note that Slant height of the pyramid= $\sqrt{(Lateraledge{)}^2-(Halfthebaseedge{)}^2}=\sqrt{(20{)}^2-(10{)}^2}=10\sqrt{3}$
Now, Lateral surface area of the pyramid = $2\times 20\times 10\sqrt{3}=400\sqrt{3}$