PERIMETERS AND AREA
PERIMETER:
The perimeter is the length of a closed curve. It is measured in centimeters, meter, kilometer etc
To find the perimeter of a shape, add the length of the sides which enclose it.
Example:
- Find the perimeter of rectangle which is 6m by 9m
solution
Consider the diagram below
There are two lengths of 6m, and two of 9m
Add these 6m + 6m + 9m + 9m = 30m
The perimeter is 30m
2. find the perimeter of the following shapes
Consider the diagram below
There are two lengths of 6m, and two of 9m
Add these 6m + 6m + 9m + 9m = 30m
The perimeter is 30m 2. find the perimeter of the following shapes
Solution
(a) The Perimeter = 4m +6m +10m +12m
(a) The Perimeter = 4m +6m +10m +12m
=32m
The perimeter is 32m (b) For the triangle
The perimeter = 4cm + 5cm +7cm
= 16cm
The perimeter = 16cm(a) In the figure below find the value of p if the perimeter is 24cm
solution.
solution.
The perimeter = 5cm +6cm +P cm +P cm
24 =16cm +2Pcm
2Pcm = 24cm – 16cm
2Pcm = 8cm
P = 4
Circumference of circles:
The perimeter of a circle is the length of its circumference.
If c is the circumference, d is the diameter, then the result is
Multiplying across by d, it become d
If radius r is given, then
NOTE:
Example
1) A Circular running track has radius 6cm. What is the length of the track?
Solution
Take
C=2x 3.14×6
C=37.68cm
(a) Circumference 88m
(b) Circumference 210m
Solution:
28m
28m
The diameter d = 28m
AREA:-
The area of a shape is the one that gives how much surface it covers.
Area is measured in square centimeters (cm) 2, square meters (m) 2, and square kilometer (km) 2……….
Rectangle:-
consider the figure below
consider the figure below
Area = length x width
= a units x b units
= ab units square
Example:
- The length of a rectangle is 55cm, and the length is 8cm. What is the area?.
Solution:
Area = length x width
= 55cm x 8cm
= 440cm2
The area of a rectangle = 440cm2
2. The area of a rectangle is 2470m2, and the length is 65m, what is the width .
2. The area of a rectangle is 2470m2, and the length is 65m, what is the width .
Solution
Given Area = 2470m2
Length = 65m
But Area = length x width
2470m2 = 65m x width
Width = 38m
The width of the rectangle is 38m.
Parallelogram
The area of a parallelogram = base x height
If base is b and height is h
Then Area = bh
The height of parallelogram is the perpendicular height.
Example
The parallelogram has base 15cm and height 22mm.What is its area? give your answer in cm
Then Area = bh
The height of parallelogram is the perpendicular height.
Example
The parallelogram has base 15cm and height 22mm.What is its area? give your answer in cm
Height = 22mm
10cm = 10mm
? = 22mm
= 2.2 cm
But Area = base x height
= 15cm x 2.2 cm
= 33cm2
The area of a parallelogram = 33cm22. A rhombus has s
ide 1.2m and height 0.8m. What are its areas?
Solution
ide 1.2m and height 0.8m. What are its areas?
Solution
But Area = base x height
=1.2m x 0.8m
= 0.96m2
The area of a rhombus = 0.96m2Triangle:-
Consider the triangle below:-
Example:
find area of triangle of below
9m2
The area = 9m2
Example:
find area of triangle of below
9m2
The area = 9m2
TRAPEZIUM
consider the parallel side of a trapezium are a and b as shown below
Then
Example; Find the area of the Trapezium below
consider the parallel side of a trapezium are a and b as shown below
Then
Example; Find the area of the Trapezium below
Solution
Where b = 20cm + 6cm
b = 26cm
a = 20cm
h = unknown
Area =184cm2
Area =184cm2
Area of a circle:-
Consider a circle with radius r shown below
If the circle has the diameter d as shown below
Then its area is
Since, d = r x r
d = 2r
If the circle has the diameter d as shown below
Then its area is
Since, d = r x r
d = 2r
Example:-
Find the area of the circle with the following measurement
(a) Diameter 8m
(b) Radius 3cm
(c) Diameter 0.2km
Solution
EXERCISE
1. find the perimeter of the shapes
1. find the perimeter of the shapes
2. find the area of these shapes
3. A ball of radius 5m rolls along the ground 100 times ,
a) How far has it traveled?
b) How many times must the ball roll for it to cover 157m?
(Take =3.14)
SOLUTIONS TO EXERCISE 1
1. a) Perimeter = 2.5cm + 8cm + 10cm + 3cm
1. a) Perimeter = 2.5cm + 8cm + 10cm + 3cm
Perimeter = 23.5cm
b) Perimeter of triangle = 8cm + 6cm +5cm
Perimeter = 19cm
Perimeter = 19cm
c) Perimeter =2 (12cm + 7cm)
= 2 x 19cm
Perimeter = 38cm
2. a) Area = base x height
Base = 2m, height = 1.5m
Area = 2m x 1.5m
= 3.0m2
Area = 3m2
Area = 6m2
a) It Rolls 100 times.
Rolling 1 time cover 31.4m
Rolling 100 times it will cover 31.4m x 100
= 3140m
It will cover 3140m
b) For the ball to cover 157m, it will roll x times
x= 5
The ball will rolls 5 times.
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