Home MATHEMATICS TOPIC 11: PERIMETERS AND AREAS ~ MATHEMATICS FORM 1

TOPIC 11: PERIMETERS AND AREAS ~ MATHEMATICS FORM 1

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The Perimeters of Triangles and Quadrilaterals

Find the perimeters of triangles and quadrilaterals
Perimeter β is defined as the total length of a closed shape. It is obtained by adding the lengths of the sides inclosing the shape. Perimeter can be measured in ππ , ππ ,ππ ,π,ππ e. t. c
Examples
Example 1
Find the perimeters of the following shapes
Solution
1. Perimeter = 7π + 7π + 3π + 3π = 20 π
2. Perimeter = 2π + 4π + 5π = 11 π
3. Perimeter = 3ππ + 6ππ + 4ππ + 5ππ + 5 ππ + 4ππ = 27 ππ

The Value of Pi ( Ξ )
Estimate the value of Pi ( Ξ )
The number Ο is a mathematical constant, the ratio of a circle’s circumference to its diameter, commonly approximated as3.14159. It has been represented by the Greek letter “Ο” since the mid 18th century, though it is also sometimes spelled out as “pi” (/paΙͺ/).
The perimeter of a circle is the length of its circumference π. π πππππππ‘ππ = πππππ’ππππππππ. Experiments show that the ratio of the circumference to the diameter is the same for all circles
The Circumference of a Circle
Calculate the circumference of a circle
Example 2
Find the circumferences of the circles with the following measurements. Take π = 3.14
1. diameter 9 ππ
3. diameter 4.5 ππ
Solution
Example 3
The circumference of a car wheel is 150 ππ. What is the radius of the wheel?
Solution
Given circumference, πΆ = 150 ππ
β΄ The radius of the wheel is 23.89 ππ
The Area of a Rectangle
Calculate the area of a rectangle
Area β can be defined as the total surface covered by a shape. The shape can be rectangle, square, trapezium e. t. c. Area is measured in mm!, cm!,dm!,m! e. t. c
Consider a rectangle of length π and width π€
Consider a square of side π
Consider a triangle with a height, β and a base, π
The Area of a Parallelogram
Calculate area of a parallelogram
A parallelogram consists of two triangles inside. Consider the figure below:
The Area of a Trapezium
Calculate the area of a trapezium
Consider a trapezium of height, β and parallel sides π and π
Example 4
The area of a trapezium is120 π!. Its height is 10 π and one of the parallel sides is 4 π. What is the other parallel side?
Solution
Given area, π΄ = 120 π2, height, β = 10 π, one parallel side, π = 4 π. Let other parallel side be, π
Then

Areas of Circle
Calculate areas of circle
Consider a circle of radius r;
Example 5
Find the areas of the following figures
Solution
Example 6
A circle has a circumference of 30 π. What is its area?
Solution
Given circumference, πΆ = 30 π
C = 2ππ
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