Area of a Rectangle

The space inside a rectangle equals its base multiplied by its height.

A = b h

Multiply the base b by the height h to fill the whole rectangle.

What each symbol means

• A: the area (space inside the rectangle)
• b: the base, or length (how wide it is along the bottom)
• h: the height, or width (how tall it is up the side)

The area of a rectangle is the easiest area to picture: just multiply the two side lengths. You will also see this written as "length times width". Base times height and length times width mean the same thing here.

The formula is A = b h. Measure the bottom, measure the side, multiply.

A worked example

A rug is 6 feet long and 4 feet wide

1. Write the formula: A = b h.
2. Put in the numbers: A = 6 × 4.
3. Multiply: 6 × 4 = 24.
4. The rug covers 24 square feet of floor.

Squares are rectangles too: A square is just a rectangle with all sides equal. So for a square with side s, the area is s × s = s².

• The area of a rectangle is A = b h (base times height, or length times width).
• It works because you are counting rows of unit squares.
• For a square, both sides are equal, so the area is s².
• Area is in square units.

Why length times width works

1. Cover the rectangle with a grid of 1-by-1 unit squares.
2. Each row has as many squares as the base is long. If the base is 6, each row holds 6 squares.
3. There are as many rows as the height is tall. If the height is 4, there are 4 rows.
4. So the total number of unit squares is 6 per row times 4 rows, which is 6 × 4 = 24. That is exactly base times height.

Practice questions

Question 1

Find the area of a rectangle 9 cm long and 5 cm wide.

1. Write the formula: A = b h (length times width).
2. Put in the numbers: A = 9 × 5.
3. Multiply to get 45.
4. The area is 45 square cm.

Answer: 45 square cm

Question 2

Find the area of a rectangle 12 m by 3 m.

1. Write the formula: A = b h (length times width).
2. Put in the numbers: A = 12 × 3.
3. Multiply to get 36.
4. The area is 36 square m.

Answer: 36 square m

Question 3

A square has a side of 7 cm. What is its area?

1. A square is a rectangle with equal sides, so its area is side times side, A = s².
2. Both sides are 7, so put in the numbers: A = 7 × 7.
3. Multiply to get 49.
4. The area is 49 square cm.

Answer: 49 square cm

Question 4

A rectangle has area 40 square cm and a base of 8 cm. What is its height?

1. Start from the formula and fill in what we know: 40 = 8 × h.
2. Undo the multiplication by dividing both sides by 8: h = 40 ÷ 8.
3. That gives h = 5.
4. The height is 5 cm.

Answer: 5 cm

Question 5

A wall is 10 feet wide and 8 feet tall. How much area needs painting?

1. The area to paint is the wall rectangle, so use A = b h.
2. Put in the width and height: A = 10 × 8.
3. Multiply to get 80.
4. The wall needs 80 square feet of paint.

Answer: 80 square feet