Math  Help

# Perimeter, Area and Volume

## What is perimeter, area, and volume?

The perimeter is the distance around the outside of an object. The area is the amount of space inside the object. The volume is the amount of space that the object occupies.

The perimeter is one dimensional, therefore its units are linear. The area is two dimensional, therefore its units are square. The volume is three dimensional, therefore its units are cubic.

## Equation of Perimeter, Area and Volume

.
Perimeter

Perimeter of a Square

P=4s, where s is the length of the side of the square.

Perimeter of a Rectangle

P=2L+2W, where L is the length and W is the width of
the sides of the rectangle.

Perimeter of a Triangle

P = a+b+c, where a, b , and c are the lengths of the sides.

Perimeter of a Circle

P=C=2πr=πd, where r is the radius and d is the diameter.

.
Area

Area of a Square

A=s2, where s is the length of the side of the square.

Area of a Rectangle

A=LW, where L is length and W is width of the sides of the rectangle.

Area of a Triangle

, where b is base and h is height.

Area of a Circle

A=πr2, where r is the radius.

.
Volume

Volume of a Cube

V=s3, where s is the length of the side.

Volume of a Sphere

, where r is the radius.

Volume of a Prism or Cylinder

V=Ah, where A is the area of the base, h is the height.

Volume of a Pyramid or Cone

, where A is the area of the base, h is the height.

## Example of Perimeter, Area and Volume

Find the perimeter of a triangle with the following side lengths: 2 cm, 5 cm, and 10 cm.

Write down the formula

P = a+b+c

Plug in the values into the formula

P = 2 cm + 5 cm + 10 cm = 17 cm

## Practice Problems ofPerimeter, Area and Volume

• Find the perimeter of a square that has a length of 5 cm.

• Find the area of a rectangle that has a length of 3 cm and a width of 5 m.

• Find the volume of a sphere that has a radius of 10 m.

## Take Home Points forPerimeter, Area and Volume

• Perimeter is defined by the distance around the outside of the object

• Area is defined by the amount of space inside the object

• Volume is defined by the space that the object takes up

• Different objects have different formulas to calculate their perimeter, area, and volume

perimeter, area and volume
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