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 [tex]\frac{1}{2} (8) = 4[/tex] 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.
[tex]12^{2} = 4^{2} +x^{2} .[/tex]
[tex]x^{2} = 12^{2} - 4^{2} = 144-16=128.[/tex]
[tex]x=\sqrt{128} = 11.313[/tex] m.
The height of the square-based pyramid is 11.313 m.
