# INTRODUCTION TO PERIMETER CIRCUMFERENCE AND AREA

Perimeter :

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

Circumference :

The perimeter of a circle or ellipse is called its circumference. In other words, the distance around the edge of a circle or any curvy shape.

Area :

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

## Perimeter, Circumference and Area Formulas

Formulas for the perimeter P, area A, circumference C of some common figures are given below.

SQUARE :

RECTANGLE :

TRIANGLE :

CIRCLE :

The measurements of perimeter and circumference 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.

## Perimeter, Circumference and Area - 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 :

Find the diameter, radius, circumference and area of the circle shown below. use 3.14 as an approximation for ∏.

Solution :

From the diagram shown above, we can see that the diameter of the circle is

d  =  13 - 5  =  8 cm

r  =  d/2  =  8/2  =  4 cm

Using the formula for circumference, we have

C  =  2∏r  ≈  2(3.14)4

C  ≈  25.1 cm

Using the formulas for area, we have

A  =  ∏r²  ≈  (3.14)(4)²

A  ≈  50.24 square cm.

Example 3 :

Find the area and perimeter of the triangle shown below.

Using the formula for perimeter of the triangle, we have

P  =  a + b + c

P  =  5 + 8 + 5

P  =  18 cm

Using the formula for area of the triangle, we have

A  =  (1/2)b⋅h

A  =  (1/2)⋅8⋅6

A  =  24 square cm.

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