Exercise 4 Page 777

A triangular prism is a prism that has triangular bases. Let's take a look at the given diagram.

The surface area of a triangular prism is the sum of the areas of the two triangular bases and the three rectangular faces. Let's calculate the area of the triangular bases and the area of the rectangular faces one at a time. Then we can add them together.

Triangular Bases

The triangular bases of the given prism are right triangles with legs that are $10$ centimeters and $12$ centimeters long. In right triangles, the legs are perpendicular, so each of the legs is also a height falling onto the other leg. Therefore, the area of a right triangle is half the product of the legs. Let's use this fact to find the area of one of the prism's bases.