# PERIMETER AND AREA OF RECTANGLE

In this section, you will learn how to find perimeter and area of a rectangle.

A rectangle is a four-sided closed figure where the lengths of opposite sides will be equal and each vertex angle will be right angle or 90o as shown below.

## Formula for Perimeter of Rectangle

Let l be the length and w be the width of a rectangle.

Then, the formula for perimeter of the rectangle :

Perimeter  =  2(l + w)

## Formula for Area of a Rectangle

To get the area of any rectangle, we have to multiply its length and width.

Let l be the length and w be the width of a rectangle.

Then, the formula for area of the rectangle :

Area  =  l ⋅ w

Example 1 :

Find the perimeter of the figure shown below.

Solution :

The figure shown above is a rectangle with 7 inches length and 11 inches width.

Formula for perimeter of a rectangle :

=  2(l + w)

Substitute 7 for l and 11 for w.

=  2(7 + 11)

=  2(18)

=  36

So, the perimeter of the rectangle is 36 inches.

Example 2 :

The perimeter of a rectangle is 42 cm. If its width is 3 more than twice its length, then find its length and with.

Solution :

Let x be the length of the rectangle.

Then, the width is (2x + 3)

Perimeter of the rectangle  =  42 cm

2(l + w)  =  42

Divide each side by 2.

l + w  =  21

Substitute x for l and (2x + 3) for w.

x + (2x + 3)  =  21

x + 2x + 3  =  21

3x + 3  =  21

Subtract 3 from each side.

3x  =  18

Divide each side by 3.

x  =  6

Therefore, the length is 6 cm.

And the width is

2x + 3  =  2(6) + 3

2x + 3  =  12 + 3

2x + 3  =  15

So, the length and width of the rectangle are 6 cm and 15 cm respectively.

Example 3 :

Find the area of the figure shown below.

Solution :

The figure shown above is a rectangle with 3 cm length and 8 cm width.

Formula for area of a rectangle :

=  l ⋅ w

Substitute 3 for l and 8 for w.

=  3 ⋅ 8

=  24

So, the area of the rectangle is 24 square cm.

Example 4 :

Find the area of the figure shown below.

Solution :

The figure shown above is a rectangle with 3 cm length and the measure of one the diagonals is √13 cm.

To find the area of a rectangle, we have to know its length and width. In the figure shown above, length is given, that is 3 cm. So, find its width.

In the figure shown above, consider the right triangle ABC.

By Pythagorean Theorem, we have

AB2 + BC2  =  AC2

Substitute.

AB2 + 32  =  (√13)2

Simplify and solve for AB.

AB2 + 9  =  13

Subtract 9 from each side.

AB2  =  4

Find positive square root on both sides.

√AB2  =  √4

AB  =  2

Therefore, the width of the rectangle is 2 cm.

Formula for area of a rectangle :

=  l ⋅ w

Substitute 3 for l and 2 for w.

=  3 ⋅ 2

=  6

So, the perimeter of the rectangle is 6 square cm.

Example 5 :

The length and width of a rectangular shaped wall are 8 ft and 12 ft respectively. If the cost of painting is \$8.50 per square feet, then find the total cost of painting for the wall.

Solution :

To find the total cost of painting for the wall, we have to know its area. Because the wall is rectangle shaped, we can use the formula for area of a rectangle to find the area of the wall.

Formula for area of a rectangle :

=  l ⋅ w

Substitute 8 for l and 12 for w.

=  8 ⋅ 12

=  96

So, the area of the wall is 96 square ft.

The cost of painting is \$8.50 per square ft.

Then, the total cost of painting for 96 square ft :

=  96 ⋅ 8.50

=  816

So, the total cost of painting the wall is \$816.

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