Question

The measurements of the lateral surface of a square pyramid are shown in the figure. What are the slant height and the base edge of the pyramid respectively?

Answer 1

By the angle sum property, it follows that the triangle is equilateral, and hence the base edge of the pyramid equals $20cm$.

Also, the triangle is isosceles implies that the altitude of the triangle face of the pyramid, or in other words the slant height of the pyramid bisects the base.

So, using Pythagoras theorem, the slant height of the triangle is
$\sqrt{{20}^2-{10}^2}=\sqrt{300}=10\sqrt{3}centimetres$