# 5.3: Square and Rectangle Area and Perimeter

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

1. Find the area and perimeter of a square with sides of length $$12\text{ in }$$.
2. Find the area and perimeter of a rectangle with height of $$9\text{ cm }$$ and base of $$16\text{ cm }$$.
3. Find the area and perimeter of a rectangle if the height is 8 and the base is 14.
4. Find the area and perimeter of a square if the sides are $$18\text{ ft }$$.
5. If the area of a square is $$81\text{ ft}^2$$, find the perimeter.
6. If the perimeter of a square is $$24\text{ in }$$, find the area.
7. The perimeter of a rectangle is 32. Find two different dimensions that the rectangle could be.
8. Draw two different rectangles that haven an area of $$90\text{ mm}^2$$.
9. True or false: For a rectangle, the bigger the perimeter, the bigger the area.
10. 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: $$P = 2b + 2h$$.