# PSAT Math : Other Polyhedrons

## Example Questions

### Example Question #1 : Other Polyhedrons

A regular octahedron has eight congruent faces, each of which is an equilateral triangle.

A given octahedron has edges of length five inches. Give the total surface area of the octahedron.

Possible Answers:

Correct answer:

Explanation:

The area of an equilateral triangle is given by the formula

Since there are eight equilateral triangles that comprise the surface of the octahedron, the total surface area is

Substitute :

square inches.

### Example Question #2 : How To Find The Surface Area Of A Polyhedron

A regular icosahedron has twenty congruent faces, each of which is an equilateral triangle.

The total surface area of a given regular icosahedron is 400 square centimeters. To the nearest tenth of a centimeter, what is the length of each edge?

Possible Answers:

Correct answer:

Explanation:

The total surface area of the icosahedron is 400 square centimeters; since the icosahedron comprises twenty congruent faces, each has area  square centimeters.

The area of an equilateral triangle is given by the formula

Set  and solve for

centimeters.

### Example Question #1 : How To Find The Volume Of A Polyhedron

The above depicts a rectangular swimming pool for an apartment. 80% of the pool is six feet deep, and the remaining part of the pool is four feet deep. How many cubic feet of water does the pool hold?

Possible Answers:

None of the other choices gives the correct answer.

Correct answer:

Explanation:

The cross-section of the pool is the area of its surface, which is the product of its length and its width:

square feet.

Since 80% of the pool is six feet deep, this portion of the pool holds

cubic feet of water.

Since the remainder of the pool - 20% - is four feet deep, this portion of the pool holds

cubic feet of water.

Add them together: the pool holds

cubic feet of water.