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 :

side length = s

Perimeter = 4s

Area = s²

Rectangle :

length = l and width = w

Perimeter = 2l + 2w

Area = lw

Triangle :

side lengths a, b and c, base = b and height = h

Perimeter = a + b + c

Area = (1/2) ⋅ b ⋅ c

Circle :

radius = r

Circumference = 2πr

Area = πr²

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.

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 π.

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 = 2πr ≈ 2(3.14)(4)

C ≈ 25.1 cm

Using the formulas for area, we have

A = πr² ≈ (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

= 5 + 8 + 5

= 18 cm

Using the formula for area of the triangle, we have

A = (1/2) ⋅ b ⋅ h

= (1/2) ⋅ 8 ⋅ 6

= 24 cm²

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