Question

Calculate the height of the square based pyramid

Answer 1

Given:

A square pyramid with a base edge length of 8 m and a slant height of 12 m.

To find:

The height of the pyramid.

Solution:

A right-angled triangle can be formed with the slant height, the height, and half the length of the base edge.

The slant height of the pyramid is 12 m long and is the hypotenuse of the right-angled triangle.

Assume the height of the pyramid is x and half the length of the base edge is $\frac{1}{2} (8) = 4$ m.

According to the Pythagorean theorem, the square of the hypotenuse will be equal to the sum of the squares of the other two sides.

The hypotenuse measures 12 m while the other two sides measure 4 m and x m each.

$12^{2} = 4^{2} +x^{2} .$

$x^{2} = 12^{2} - 4^{2} = 144-16=128.$

$x=\sqrt{128} = 11.313$ m.

The height of the square-based pyramid is 11.313 m.