Trapezoid Prism Problems

Category: Solid Geometry

"Published in Vacaville, California, USA"

A trench is 180 ft. long and 12 ft. deep, 7 ft. wide at the top and 4 ft. at the bottom. How many cubic yards of earth have been removed?

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

The amount of earth removed is in the shape of a prism whose base is a trapezoid. The area of the base which is a trapezoid is

The amount of earth removed which is the volume of a trapezoid prism is

Therefore, the amount of earth removed in cubic yards is

Polygon Prism Problems, 3

Category: Solid Geometry

"Published in Vacaville, California, USA"

One part of a quartz crystal is a hexagonal prism with a right section of 1.29 sq. in., an edge of 2.31 in., and a base of 1.41 sq. in. Find the altitude of the prism.

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

The volume of a quartz crystal is

Therefore, the altitude of a quartz crystal is

Polygon Prism Problems, 2

Category: Solid Geometry

"Published in Vacaville, California, USA"

The lateral surface of a concrete octagonal pier of height 10 ft. is to be resurfaced. If each of the base edges is 1 ft., how many square feet of surfacing will be required?

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday life

The lateral surface area of a concrete octagonal pier required to be resurfaced is