Question

Find the volume of the square pyramid, if one the triangular faces is given below.

Answer 1

Since the triangular face is isosceles, the altitude bisects the base.

The slant height can be calculated as:

$\Rightarrow \sqrt{(\sqrt{353}{)}^2-8^2}\Rightarrow \sqrt{353-64}\Rightarrow \sqrt{289}=17$

Given the slant height, we have to calculate the height of the pyramid. Hence,

$h^2={17}^2-8^2\Rightarrow h^2=289-64\Rightarrow h=\sqrt{225}=15$

Now, the dimensions of the pyramid are: $a=16cm,h=15cm$

Volume $=\frac{1}{3}(16{)}^2.15=\frac{1}{3}\times 256\times 15=1280c{m}^3$