MATHEMATICS Form 1 Topic 11
PERIMETERS AND AREAS
The Perimeters of Triangles and Quadrilaterals
Find the perimeters of triangles and quadrilaterals
Perimeter – 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 ?? , ?? ,?? ,?,?? e. t. c
Examples
Example 1
Find the perimeters of the following shapes
Solution
- Perimeter = 7? + 7? + 3? + 3? = 20 ?
- Perimeter = 2? + 4? + 5? = 11 ?
- Perimeter = 3?? + 6?? + 4?? + 5?? + 5 ?? + 4?? = 27 ??
The Value of Pi ( Π)
Estimate the value of Pi ( Π)
The number π 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 “π” since the mid 18th century, though it is also sometimes spelled out as “pi” (/paɪ/).
The perimeter of a circle is the length of its circumference ?. ? ????????? = ?????????????. 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 ? = 3.14
- diameter 9 ??
- radius 3½?
- diameter 4.5 ??
- radius 8 ??
Solution
Example 3
The circumference of a car wheel is 150 ??. What is the radius of the wheel?
Solution
Given circumference, ? = 150 ??
∴ The radius of the wheel is 23.89 ??
The Area of a Rectangle
Calculate the area of a rectangle
Area – 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 ? and width ?
Consider a square of side ?
Consider a triangle with a height, ℎ and a base, ?
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, ℎ and parallel sides ? and ?
Example 4
The area of a trapezium is120 ?!. Its height is 10 ? and one of the parallel sides is 4 ?. What is the other parallel side?
Solution
Given area, ? = 120 ?2, height, ℎ = 10 ?, one parallel side, ? = 4 ?. Let other parallel side be, ?
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 ?. What is its area?
Solution
Given circumference, ? = 30 ?
C = 2??
