The pyramid shown has a square base that is 12 centimeters on each side. The slant height is 18 centimeters. What is the surface area of the pyramid?

The correct answer is:

576 sq. cm.

Explanation:

The surface area of a figure is the sum of the areas of the faces of the figure.

The slant height goes from the apex of the pyramid along a face and is perpendicular to the base at the bottom of that face. This gives us 2 measurements of each triangular face of the pyramid: the height (the slant height of the pyramid is the height of the triangular face), 18 cm, and the base of the triangular face, 12 cm.

The formula for the area of a triangle is A = 1/2bh; using our measurements we have:

A = 1/2 (12) (18) = 108 sq. cm.

There are 4 triangular faces on a square pyramid, and each will have an area of 108 sq. cm.; this gives us:

4 (108) = 432 sq. cm.

The area of the base is given by length times width, or 12*12 = 144 sq. cm.

This gives us a total surface area of 432+144=576 sq. cm.