Question

A right pyramid stands on a rectangular base whose sides are 24 cm and 18 cm and each of the slant edges is 17 cm. the height of the pyramid is
A. 8
B. 10
C. 12
D. 15

Answer 1

Hint: We first use the Pythagoras’ theorem to find the diagonal of the rectangular base. We use the half length of the diagonal to use the theorem again to find the height of the pyramid. We take the sides as the slant height and actual height of the pyramid.

Complete step by step solution:
The base of the given pyramid is of a rectangular base. We first try to find the length of the diagonal of the rectangular base.
The sides of the base are 24 cm and 18 cm.
We know that for a rectangle with sides a and b, the length of the diagonal will be $\sqrt{{{a}^{2}}+{{b}^{2}}}$.
So, for the rectangle the diagonal will be $\sqrt{{{24}^{2}}+{{18}^{2}}}=\sqrt{900}=30$ cm.
Now we draw the pyramid where the half of a diagonal with the slant height and the height makes the right-angle triangle.

The half of the diagonal is $\dfrac{30}{2}=15$ cm.
We now use the Pythagoras’ theorem which gives the height as $\sqrt{{{17}^{2}}-{{15}^{2}}}=\sqrt{64}=8$.
So, the correct answer is “Option A”.

Note: In some cases, you may need to find the height of your pyramid before you’re able to work out its volume. Let’s say you’re given the slant height of the pyramid, which is the distance from the apex to the centre of one of the triangular faces.