# FINDING THE PERIMETER AND AREA OF A RECTANGLE

Perimeter :

Perimeter is a path that surrounds a rectangle. The term may be used either for the path or its length it can be thought of as the length of the outline of the rectangle.

Area :

Area of a rectangle is defined as the space occupied by the rectangle shaped object on a flat surface. The area of a shape can be measured by comparing the shape to squares of a fixed size.

## Formulas for Perimeter and Area of a Rectangle

The measurements of perimeter use units such as centimeters, meters, kilometers, inches, feet, yards, and miles. The measurements of area use units such as square centimeters (cm²), square meters(m²), and so on.

## Examples

Example 1 :

Find the perimeter and area of a rectangle of length 12 inches and width 5 inches.

Solution :

Draw a rectangle and label the length and width.

 Perimeter  =  2l + 2wPerimeter  =  2(12) + 2(5)Perimeter  =  24 + 10Perimeter  =  34 Area  =  lwArea  =  12⋅5 Area  =  60

So, the perimeter is 34 inches and the area is 60 square inches.

Example 2 :

The area of a rectangle is 56 square inches. If the length is 8 inches, find the width of the rectangle.

Solution :

Given :  Area of the rectangle  =  56 sq. in

lw  =  56

Substitute l = 8

8w  =  56

Divide both sides by 8.

w  =  7

So, the width is 7 inches.

Example 3 :

The perimeter of a rectangle is 30 cm. The length is 3 more than twice the width. Find the length and width of the rectangle.

Solution :

Step 1 :

Let w  =  x.

Then, l  =  2x + 3

Step 2 :

Given :  Perimeter of the rectangle  =  30 cm

2l + 2w  =  30

Step 3 :

Substitute w = x and l = 2x + 3

2(2x + 3) + 2x  =  30

4x + 6 + 2x  =  30

6x + 6  =  30

Subtract 6 from both sides.

6x  =  24

Divide both sides by 6.

x  =  4

Width  =  x  =  4

Length  =  2x + 3  =  2(4) + 3  =  11

So, the length is 11 cm and width is 4 cm.

Example 4 :

The diagonal of a rectangle is 5 cm and one of its sides is 4 cm. Find its area.

Solution :

Step 1 :

Let us assume that one of the sides given is length.

Then, l  =  4 cm.

Step 2 :

Draw a rectangle and label the diagonal and length.

Step 3 :

To find area of a rectangle, we need the measures of length and width. We know the length and it is 4 cm. We have to find the width.

Step 4 :

In the rectangle above, let us consider the right triangle ABC and apply Pythagorean theorem.

AB² + BC²  =  AC²

Substitute BC  =  4 and AC  =  6

w² + 4²  =  5²

w² + 16  =  25

Subtract 16 from both the sides.

w²  =  9

w²  =  3²

Remove the exponent 2 on both sides.

w  =  3 cm.

Step 5 :

Area of the rectangle  =  lw

Area of the rectangle  =  4⋅3

Area of the rectangle  =  12 square cm.

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