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# Area and Perimeter of Rectangles

## Area is base times height, while perimeter is the sum of the sides.

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Area and Perimeter of Rectangles

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? After completing this Concept, you'll be able to use the formulas for the perimeter and area of a rectangle to solve problems like this.

### Watch This

Area and Perimeter of Rectangles CK-12

### Guidance

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

If a rectangle is a square, with sides of length s\begin{align*}s\end{align*}, then perimeter is Psquare=2s+2s=4s\begin{align*}P_{square}=2s+2s=4s\end{align*} and area is Asqaure=ss=s2\begin{align*}A_{sqaure}=s \cdot s=s^2\end{align*}.

#### Example A

Find the area and perimeter of a rectangle with sides 4 cm by 9 cm.

The perimeter is 4+9+4+9=26 cm\begin{align*}4 + 9 + 4 + 9 = 26 \ cm\end{align*}. The area is A=94=36 cm2\begin{align*}A=9 \cdot 4=36 \ cm^2\end{align*}.

#### Example B

Find the area and perimeter of a square with side 5 in.

The perimeter is 4(5)=20in\begin{align*}4(5)=20in\end{align*} and the area is 52=25 in2\begin{align*}5^2=25 \ in^2\end{align*}.

#### Example C

Find the area and perimeter of a rectangle with sides 13 m and 12 m.

The perimeter is 2(13)+2(12)=50 m\begin{align*}2(13)+2(12)=50 \ m\end{align*}. The area is 13(12)=156 m2\begin{align*}13(12)=156 \ m^2\end{align*}.

Area and Perimeter of Rectangles CK-12

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### Guided Practice

1. The area of a square is 75 in2\begin{align*}75 \ in^2\end{align*}. Find the perimeter.

2. Draw two different rectangles with an area of 36 cm2\begin{align*}36 \ cm^2\end{align*}.

3. Find the area and perimeter of a rectangle with sides 7 in and 10 in.

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

As=s2=75 in2=75=53 in

From this, P=4(53)=203 in\begin{align*}P=4 \left (5\sqrt{3} \right )=20\sqrt{3} \ in\end{align*}.

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

Other possibilities could be 6×6,2×18\begin{align*}6 \times 6, 2 \times 18\end{align*}, and 1×36\begin{align*}1 \times 36\end{align*}.

3. Area is 7(10)=70 in2\begin{align*}7(10)=70 \ in^2\end{align*}. Perimeter is 2(7)+2(10)=34 in\begin{align*}2(7)+2(10)=34 \ in\end{align*}.

### Explore More

1. Find the area and perimeter of a square with sides of length 12 in.
2. Find the area and perimeter of a rectangle with height of 9 cm and base of 16 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 ft.
5. If the area of a square is 81 ft2\begin{align*}81 \ ft^2\end{align*}, find the perimeter.
6. If the perimeter of a square is 24 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 mm2\begin{align*}90 \ mm^2\end{align*}.
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 in and 21 in.

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 10.1.

### Vocabulary Language: English Spanish

area

area

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

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

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

Perimeter of a Rectangle

The perimeter 'P' of a rectangle is equal to twice the base added to twice the height: P = 2b + 2h.