Exercise 1 Page 422

We want to calculate the surface area of a square pyramid. Let's see the given measurements of the pyramid.

We can use a net to calculate the surface area of the pyramid. Let's draw a net!

The net is made up of a square and four triangles. Let's calculate the area of each polygon separately, starting with the square.

The area of the square base is 81 square centimeters. Now let's take a look at the triangles. Notice that the lateral faces of the pyramid are identical triangles. This means that they have the same area. Let's substitute the measures of the lateral faces into the formula for the area of a triangle!

We found that the area of one triangle is 31.5 square centimeters. Since the triangles are identical, the area of each triangle is 31.5 square centimeters. We now have all the information that we need to find the total surface area of the square pyramid! Total Surface Area 81+ 31.5+ 31.5+ 31.5+ 31.5=207cm^2 The total surface area of the square pyramid is 207 square centimeters.