# 5.3: Square and Rectangle Area and Perimeter

- Page ID
- 2155

Compute edge and coverage measures of rectilinear quadrilaterals, given linear measures.

## Area and **Perimeter** of Rectangles

To find the **area of a rectangle**, calculate \(A=bh\), where \(b\) is the base (width) and \(h\) is the height (length). The **perimeter of a rectangle** will always be \(P=2b+2h\).

If a rectangle is a square, with sides of length s, then perimeter is \(P_{square}=2s+2s=4s\) and area is \(A_{sqaure}=s\cdot s=s^2\).

What if you were given a rectangle and the size of its base and height? How could you find the total distance around the rectangle and the amount of space it takes up?

Example \(\PageIndex{1}\)

The area of a square is \(75\text{ in}^2\). Find the perimeter.

**Solution**

To find the perimeter, we need to find the length of the sides.

\(\begin{aligned} A&=s^2=75\text{ in}^2 \\ s&=\sqrt{75}=5\sqrt{3}\text{ in } \end{aligned}\)

From this, \(P=4(5\sqrt{3})=20\sqrt{3}\text{ in }\)

Example \(\PageIndex{2}\)

Draw two different rectangles with an area of \(36\text{ cm^2 }\).

**Solution**

Think of all the different factors of 36. These can all be dimensions of the different rectangles.

Other possibilities could be \(6\times 6\), \(2\times 18\), and \(1\times 36\).

Example \(\PageIndex{3}\)

Find the area and perimeter of a rectangle with sides \(4\text{ cm }\) by \(9\text{ cm }\).

**Solution**

The perimeter is \(4+9+4+9=26\text{ cm }\). The area is \(A=9\cdot 4=36\text{ cm}^2\).

Example \(\PageIndex{4}\)

Find the area and perimeter of a square with side \(5\text{ in }\).

**Solution**

The perimeter is \(4(5)=20\:in\) and the area is \(5^2=25\text{ in}^2\).

Example \(\PageIndex{5}\)

Find the area and perimeter of a rectangle with sides \(13\text{ m }\) and \(12\text{ m}^2\).

**Solution**

The perimeter is \(2(13)+2(12)=50\text{ m }\). The area is \(13(12)=156\text{ m}^2\).

## Review

- Find the area and perimeter of a square with sides of length \(12\text{ in }\).
- Find the area and perimeter of a rectangle with height of \(9\text{ cm }\) and base of \(16\text{ cm }\).
- Find the area and perimeter of a rectangle if the height is 8 and the base is 14.
- Find the area and perimeter of a square if the sides are \(18\text{ ft }\).
- If the area of a square is \(81\text{ ft}^2\), find the perimeter.
- If the perimeter of a square is \(24\text{ in }\), find the area.
- The perimeter of a rectangle is 32. Find two different dimensions that the rectangle could be.
- Draw two different rectangles that haven an area of \(90\text{ mm}^2\).
- True or false: For a rectangle, the bigger the perimeter, the bigger the area.
- Find the perimeter and area of a rectangle with sides \(17\text{ in }\) and \(21\text{ in }\).

## Vocabulary

Term | Definition |
---|---|

area |
The amount of space inside a figure. Area is measured in square units. |

perimeter |
The distance around a shape. The perimeter of any figure must have a unit of measurement attached to it. If no specific units are given (feet, inches, centimeters, etc), write units. |

Area of a Rectangle |
To find the area '\(A\)' of a rectangle, calculate \(A = bh\), where \(b\) is the base (width) and h is the height (length). |

Perimeter of a Rectangle |
The perimeter '\(P\)' of a rectangle is equal to twice the base added to twice the height: \(P = 2b + 2h\). |

## Additional Resources

Interactive Element

Video: Determine the Area of a Rectangle Involving Whole Numbers

Activities: Area and Perimeter of Rectangles Discussion Questions

Study Aids: Triangles and Quadrilaterals Study Guide

Practice: Square and Rectangle Area and Perimeter

Real World: Perimeter