Question

A pentagonal prism has a base area of 124 square inches. The lateral area (area of the sides) is made up of 5 equal-sized rectangles that are each 80 square inches. What is the surface area of the pentagonal prism?

Answer 1

The surface area of the pentagonal prism is 648 square inches.

Step-by-step explanation:

Step 1:

The surface area of a shape is the sum of all the areas of all the external surfaces.

The pentagonal prism has a total of 7 sides i.e. 2 pentagonal sides and 5 rectangular sides.

The total surface area of the prism is the sum of the individual areas of the 7 sides.

Step 2:

The area of the 2 pentagonal sides $= 2(124) = 248$ square inches.

The area of each rectangular side is 80 square inches. So

The area of 5 rectangular sides $= 5(80) = 400$ square inches.

The total surface area of the prism $=248+400 = 648$ square inches.

The surface area of the pentagonal prism is 648 square inches.