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# Geometry for Praxis II ParaPro Test Prep Study Guide (page 2)

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Updated on Mar 16, 2011

### Perimeter

To find the perimeter of a figure, simply add up the lengths of all of its sides.

Example
What is the perimeter of the following triangle?

The triangle has side lengths of 5, 8, and 10. The perimeter is therefore the sum of 5 + 8 + 10. The perimeter of the triangle is 23.

### Circumference

The circumference is the distance around a circle. The circumference can be found by multiplying the diameter of the circle by pi, or π, a special number equal to about 3.14. It can also be found by multiplying the radius of the circle by 2 and then by π. The formulas for the circumference of a circle are circumference = 2πr and circumference = dπ, where r is the radius and d is the diameter of the circle.

Example
What is the circumference of a circle with a radius of 5?
Following the formula area = 2πr, the circumference is equal to 2(5) π, which is equal to 10π

### Area

The area is the amount of space inside a two-dimensional shape.

To find the area of a rectangle, you need to multiply the length of the rectangle times the width. The formula is area = length × width, or area = lw.

To find the area of a triangle, you need to multiply times the base of the triangle times its width. The formula is area = base × width, or area = ()lw.

To find the area of a circle, you need to multiply the radius by itself (or square it), and then multiply it by π. The formula is area = πr2, where r is the radius of the circle.

Example
What is the area of the following rectangle?

To find the area of a rectangle, multiply the length by the height. Because the length is 12 and the height is 5, the area is therefore 12 ×5, or 60 square units.

Example
What is the area of the following triangle?

The base of the triangle is 8 and its height is 5. To find the area, just plug in those known values into the formula area = lw. You will get area = (8)(5), which is equal to 20. The area is 20 square units.

Example
What is the area of a circle with a radius of 2?
Plug in the value of the radius into the formula for the area of a circle: area = πr2. You will get area = π22, which is equal to 4π.

### Volume

Volume is the amount of space inside a three-dimensional shape. To find the volume of a rectangular solid, you need to multiply the length times the width times the height.

Example
What is the volume of the following cube?

To find the volume, you need to multiply the length times the width times the height. Each dimension of the cube is 4, so the volume is 4 ×4 ×4, or 64 cubic units.

The practice quiz for this study guide can be found at:

Math for Praxis II ParaPro Test Prep Practice Problems