Question

A square pyramid covers an area of $400m^2$ on the ground and height of the pyramid is 10 m. Then find its total surface area of the pyramid

• A. $200(1+\sqrt{2})m^2$
• B. $400(1+\sqrt{2})m^2$
• C. $400(1+\sqrt{6})m^2$
• D. $200(1+\sqrt{6})m^2$

Answer 1

The correct option is B

$400(1+\sqrt{2})m^2$

Given, Area of the base (Square) = $400m^2$ ; Base edge = $\sqrt{400}=20m$ Slant height = $\sqrt{(heightofpyaramid{)}^2+(\frac{baseedge}{2}{)}^2}$

Height of pyramid = 10 m. Slant height = $\sqrt{{10}^2+{10}^2}=10\sqrt{2}$

$Totalsurfacearea=basearea+4\times (\frac{1}{2}\times base\times slantheight$ = $400+4\times (\frac{1}{2}\times 20\times 10\sqrt{2})$

= $400+400\sqrt{2}=400(1+\sqrt{2})m^2$