**Perimeter and Area of Rectangle :**

In this section, we are going to 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 90^{o }as shown below.

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)**

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

AB^{2} + BC^{2} = AC^{2}

Substitute.

AB^{2} + 3^{2} = (√13)^{2}

Simplify and solve for AB.

AB^{2} + 9 = 13

Subtract 9 from each side.

AB^{2} = 4

Find positive square root on both sides.

√AB^{2} = √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.

After having gone through the stuff given above, we hope that the students would have understood, "Perimeter and Area of Rectangle".

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