TOPIC 11: PERIMETERS AND AREASΒ
Perimeters of Triangles and Quadrilaterals
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 inββΒ πββΒ ,ββΒ ππββΒ ,ππββΒ ,π,ππββΒ e. t. c
Examples
Example 1
Find the perimeters of the following shapes
Solution
Perimeter = 7πββΒ + 7πββΒ + 3πββΒ + 3πββΒ = 20ββΒ π
Perimeter = 2πββΒ + 4πββΒ + 5πββΒ = 11ββΒ π
Perimeter = 3ππββΒ + 6ππββΒ + 4ππββΒ + 5ππββΒ + 5ββΒ ππββΒ + 4ππββΒ = 27ββΒ ππ
Circumference of a Circle
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 circumferenceββΒ π.ββΒ πββΒ πππππππ‘ππββΒ =ββΒ πππππ’ππππππππ. 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. TakeββΒ πββΒ = 3.14
diameter 9ββΒ ππ
radius 3Β½π
diameter 4.5ββΒ ππ
radius 8ββΒ ππ
Solution
Example 3
The circumference of a car wheel is 150ββΒ ππ. What is the radius of the wheel?
Solution
Given circumference,ββΒ πΆββΒ = 150ββΒ ππ
β΄ββΒ The radius of the wheel is 23.89ββΒ ππ
Areas of Rectangles and Triangles
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 lengthββΒ πββΒ and widthββΒ π€
Consider a square of sideββΒ π
Consider a triangle with a height,ββΒ βββΒ and a base,ββΒ π
Areas of Trapezium and Parallelogram
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,ββΒ βββΒ and parallel sidesββΒ πββΒ andββΒ π
Example 4
The area of a trapezium is120ββΒ π!. Its height is 10ββΒ πββΒ and one of the parallel sides is 4ββΒ π. What is the other parallel side?
Solution
Given area,ββΒ π΄ββΒ = 120ββΒ π2, height,ββΒ βββΒ = 10ββΒ π, one parallel side,ββΒ πββΒ = 4ββΒ π. Let other parallel side be,ββΒ π
Then
Area of a Circle
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 30ββΒ π. What is its area?
Solution
Given circumference,ββΒ πΆββΒ = 30ββΒ π
C = 2ππ
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