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
`(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=√(128) = 11.313` m.

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