Question

A square pyramid covers an area of $400m^2$ on the ground.
If the height of the pyramid is 10 m, then find the total surface area of the pyramid.

Answer 1

Given:
Base area of square pyramid $=400m^2$
$\Rightarrow {\text{Base edge}}^2=400$
$\Rightarrow \text{Base edge}=\sqrt{400}=20m$

Also, the height of the pyramid = 10 m

$\text{Slant height}=\sqrt{(heightofpyramid{)}^2+(\frac{baseedge}{2}{)}^2}$

Slant height $=\sqrt{{10}^2+{10}^2}=10\sqrt{2}$

Therefore,
$\text{Total surface area of pyramid}$
$=\text{Base area}+4\times (\frac{1}{2}\times \text{base edge}\times \text{slant height})$
$=400+4\times (\frac{1}{2}\times 20\times 10\sqrt{2})$
$=400+400\sqrt{2}$
$=400+565.68$
$=965.68m^2$