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 :
side length = s
Perimeter = 4s
Area = s^{2}
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 = πr^{2}
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 (cm^{2}), square meters(m^{2}), 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 = 2(12) + 2(5) = 24 + 10 = 34 |
Area = lw = 12 ⋅ 5 = 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 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 = πr^{2} ≈ (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 cm^{2}
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