**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.

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.

**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 + 2w Perimeter = 2(12) + 2(5) Perimeter = 24 + 10 Perimeter = 34 |
Area = lw Area = 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

The radius is one half the diameter. So, the radius is

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.

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

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