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Home > GC > Chapter 10 > Lesson 10.1.4 > Problem 10-41


Calculate the total surface area and volume of the prism below. Assume that the base is a regular pentagon.
Pentagonal prism, with front edge of pentagon labeled, 6 feet, and height labeled, 12 feet.

Find the central angle of the pentagon.

Area of the triangle ft
Area of pentagon ft

Find the area of each of the sides, and sum them to find the surface area.


Multiply the area of the pentagon by the height to find the volume.

The area of the triangle will help you find the area of the pentagon.

A triangle, with bottom side labeled, 6, and dashed line segment, labeled, h, from top vertex, perpendicular to the base, creating 2 right triangles. In the right triangle, on the right, the top angle is labeled, 36 degrees.

Volume ft
Surface area ft