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Home > CCG > Chapter 10 > Lesson 10.1.4 > Problem 10-46

10-46.

Calculate the total surface area and volume of the prism at right. Assume that the base is a regular pentagon.  

Find the central angle of the pentagon.

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.

,

Area of the triangle
Area of pentagon

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.

Volume
Surface area

Pentagonal prism, with front edge of pentagon labeled, 6 feet, and height labeled, 12 feet.