Area and perimeter of rectangles

Step 5 · Multiplication and first fractions topics

Find the area of a rectangle by counting squares or multiplying, find its perimeter by adding the sides, and see that the two measure different things.

Area: squares inside

Area is how much flat space a shape covers. Measure it by counting the unit squares that cover the shape with no gaps and no overlaps.

A rectangle 5 units long and 3 units wide is covered by 15 unit squares.

A rectangle is an array of squares, so multiply: length × width. 5 × 3 = 15 square units. If each square is 1 centimeter on a side, the area is 15 square centimeters.

Example: Area of a rug

A rug is 6 feet long and 4 feet wide. What is its area?

Area = length × width.
6 × 4 = 24.

Answer24 square feet

For an L-shape, cut it into two rectangles, find the area of each, and add.

An L-shape cut into a 5 by 2 rectangle and a 2 by 4 rectangle: 10 + 8 = 18 square units.

Perimeter: the distance around

Perimeter is the distance all the way around a shape. Add the lengths of all its sides.

Example: Perimeter of a garden

A garden is 7 meters long and 4 meters wide. What is its perimeter?

A rectangle has two lengths and two widths.
7 + 4 + 7 + 4 = 22.

Answer22 meters

Same area, different perimeter

Rectangles with the same area can have different perimeters. All three of these cover 12 squares.

Rectangle	Area	Perimeter
6 by 2	12	16
4 by 3	12	14
12 by 1	12	26

Three rectangles with an area of 12 square units and different perimeters.

The long, thin rectangle has the longest perimeter; the one closest to a square has the shortest. It works the other way too: rectangles with the same perimeter can have different areas.

Example: Finding a missing side

A rectangle has an area of 24 square inches and a length of 8 inches. How wide is it?

Length × width = area.
8 × ? = 24.
8 × 3 = 24.

Answer3 inches

Try it yourself

Work each one on paper first, then open the answer to check.

A rectangle is 9 cm long and 3 cm wide. What is its area?
Show answer
27 square centimeters.
What is the perimeter of the same rectangle?
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24 centimeters. 9 + 3 + 9 + 3 = 24.
A square has sides of 5 m. What are its area and its perimeter?
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Area 25 square meters; perimeter 20 meters.
A rectangle has an area of 20 square feet and a width of 4 feet. What is its length?
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5 feet.
Give two different rectangles with an area of 16 square units.
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For example 4 by 4 and 8 by 2. 16 by 1 works too.