Math Core

Counting squares one by one works, but it gets slow for big shapes. A rectangle's squares are lined up in neat rows, just like an array. That means you can multiply to find its area.

Rectangles are arrays

Look at this rectangle covered with unit squares.

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It has 3 rows with 6 squares in each row. That is an array! Instead of counting all the squares, multiply:

3 \times 6 = 18

The area is 18 square units.

Side lengths tell you the rows

Often you won't see the squares. You will only see the side lengths. That's enough.

A rectangle 4 units long and 3 units wide. The unit squares make 3 rows of 4.

A side that is 4 units long has room for 4 unit squares. A side that is 3 units long has room for 3 rows. So the rectangle holds $3 \times 4 = 12$ unit squares.

Area of a rectangle

To find the area of a rectangle, multiply the two side lengths.

\text{Area} = \text{length} \times \text{width}

Write the answer in square units.

You can multiply in either order. A rectangle 3 units by 4 units has the same area as one 4 units by 3 units, because $3 \times 4 = 4 \times 3$ .

Worked example: Multiply the sides

A rectangle is 7 centimeters long and 2 centimeters wide. What is its area?

Multiply the side lengths: $7 \times 2 = 14$ .

The area is 14 square centimeters.

Worked example: A square

A square has sides that are each 6 inches long. What is its area?

All 4 sides of a square are the same length. So both side lengths are 6.

$6 \times 6 = 36$

The area is 36 square inches.

Worked example: A real floor

A bedroom floor is a rectangle 9 feet long and 8 feet wide. How many square feet of carpet cover the floor?

$9 \times 8 = 72$

The carpet covers 72 square feet.

Finding a missing side

Sometimes you know the area and one side. Use division, or think of a missing factor.

Worked example: What is the other side?

A rectangle has an area of 24 square meters. One side is 4 meters. How long is the other side?

Think: $4 \times ? = 24$ . Since $4 \times 6 = 24$ , the other side is 6 meters.

You can also divide: $24 \div 4 = 6$ .

Common mistake

Don't add the side lengths. For a rectangle 5 by 3, $5 + 3 = 8$ is wrong. Area counts all the squares inside, so multiply: $5 \times 3 = 15$ square units.

Tip

Check your answer with a quick sketch. Draw the rows and count by the row length. For 3 rows of 6, count 6, 12, 18.

Practice

Practice 1

A rectangle is 6 units long and 3 units wide. What is its area, in square units?

Type a number.

Practice 2

Which shows how to find the area of a rectangle that is 8 feet long and 2 feet wide?

Practice 3

A card is 7 centimeters long and 4 centimeters wide. What is its area, in square centimeters?

Type a number.

Practice 4

A square tile has sides that are each 5 inches long. What is its area, in square inches?

Type a number.

Practice 5

A garden is 9 meters long and 6 meters wide. What is its area, in square meters?

Type a number.

Practice 6

A rectangle has an area of 32 square feet. One side is 4 feet long. How long is the other side, in feet?

Type a number.

Practice 7

A kitchen floor is covered with square tiles. There are 10 rows of tiles with 7 tiles in each row. Each tile is 1 square foot. What is the area of the floor, in square feet?

Type a number.

Practice 8

Rug A is 6 feet by 4 feet. Rug B is a square with 5-foot sides. How many more square feet does the bigger rug cover?

Type a number.