Question

The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being 20 cm. The vertical height of the pyramid, in cm, is

• A. \(8\sqrt{3}\)
• B. 12
• C. \(5\sqrt{5}\)
• D. \(10\sqrt{2}\)

Answer 1

The Correct Option is D

From the diagram, it is evident that AB serves as both the height of the equilateral triangle and the slant height of the pyramid.

So, \(AB=\frac{\sqrt{3}}{2}×side=\frac{\sqrt{3}}{2}×20=10\)

And \(AO=\frac{1}{2}×side=\frac{1}{2}×20=10\)
Applying Pythagoras theorem in triangle AOB

\(OB^2=AB^2−OA^2\)
\(=(10\sqrt{3})^2−10^2\)
\(=200\)

Hence, the height of the pyramid \((OB) =10\sqrt{2}\)