# Area of Rectangles and Squares

If you took the time to count all the squares, you should see that there are 48. That means that the area of the

However, counting the squares is not a very efficient way to determine the area. There is a better way.

**rectangle**, or the space that covers the rectangle, is 48 square units.However, counting the squares is not a very efficient way to determine the area. There is a better way.

**A = lw**

A = 8 units x 6 units

A = 48 square units or 48 unitsA = 8 units x 6 units

A = 48 square units or 48 units

^{2}A special type of rectangle, called a

**square**, has four equal sides.

Because the sides are equal, when we multiply the length and width, we get a number times itself, or a number squared.

So for squares, we can simplify the formula and

use A = s

Here are some more examples:

To determine the area of a rectangle, we must multiply the length and width.

We use the formula A = lw. If we are given the area and one side, we can work backwards by dividing to determine the length of the other side.

To determine the area of a square, we could use the rectangle formula, or we can use a special formula: A = s

use A = s

^{2}.**A = s**

A = (8 units)

A = 64 units

^{2}A = (8 units)

^{2}A = 64 units

^{2}Here are some more examples:

1.) Calculate the area of a rectangle with a length of 4 and a width of 9 units.

**Solution: A = lw**

A = (4 units)(9 units)

A = 36 units

A = (4 units)(9 units)

A = 36 units

^{2}2.) Determine the area of the rectangle

**Solution: A = lw**

A = (3 in)(18 in)

A = 54 in

A = (3 in)(18 in)

A = 54 in

^{2}3.) The area of a rectangle is 30 cm

^{2}and the length is 6 cm. What is the width of the rectangle?**Solution: Because we are given the area, work backwards by dividing.**

A = lw

30 cm

30 cm

5 cm = w

A = lw

30 cm

^{2}= (6 cm)w30 cm

^{2}÷ 6 cm = w5 cm = w

4.) Determine the area of a square with a side length 10 cm.

**A = s**

A = (10 cm)

A = 100 cm

^{2}A = (10 cm)

^{2}A = 100 cm

^{2}5.) Determine the area of the shape shown.

**A = s**

A = (7 mm)

A = 49 mm

^{2}A = (7 mm)

^{2}A = 49 mm

^{2}6.) The area of a square is 144 in

^{2}. What is the length of each side?**Solution: Because we are given the area, work backwards by taking the square root.**

A = s

144 in

√144 in

12 in = s

A = s

^{2}144 in

^{2}= s^{2}√144 in

^{2}= √s^{2}12 in = s

7.) The area of a square is 225 cm

^{2}. What is the perimeter?**Solution: to determine the perimeter, we must first determine the side length. Then use the side length to determine the perimeter.**

A = s

225 cm

√225 cm

15 cm = s

A = s

^{2}P = 4s225 cm

^{2}= s^{2}P = 4(15 cm)√225 cm

^{2}= √s^{2}P = 60 cm15 cm = s

**Let's Review**To determine the area of a rectangle, we must multiply the length and width.

We use the formula A = lw. If we are given the area and one side, we can work backwards by dividing to determine the length of the other side.

To determine the area of a square, we could use the rectangle formula, or we can use a special formula: A = s

^{2}. If we are given the area of a square, we can work backwards, or take the square root to determine the side length.
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