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5: Quadrilaterals and Polygons
5.3: Square and Rectangle Area and Perimeter

5.3: Square and Rectangle Area and Perimeter

Last updated

Nov 28, 2020
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- 5.2: Rectangles
- 5.4: Perimeter of Squares and Rectangles

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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 $P=2b+2h$ .

f-d_0c9a79962fc5723da8c0215d936990f9fea47b63d4511708daa10731+IMAGE_TINY+IMAGE_TINY.png — Figure $\PageIndex{1}$

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

f-d_7ca9b8bf62b2e92936dd2e410390a2f666a3a0eef8c17ea45ba02cf8+IMAGE_TINY+IMAGE_TINY.png — Figure $\PageIndex{2}$

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.

f-d_a010a8c55e067fc941596fc82902aae27eb7d1d59bbd8bfa870e5573+IMAGE_TINY+IMAGE_TINY.png — Figure $\PageIndex{3}$

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 $9\text{ cm }$ .

f-d_feea629789b7999660f1e278d4abb1a454e6ffd1b9eceb308598ce40+IMAGE_TINY+IMAGE_TINY.png — Figure $\PageIndex{4}$

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

Area and Perimeter of Rectangles

Review

Vocabulary

Additional Resources

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