Perimeters And Areas

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

1. Perimeter = 7? + 7? + 3? + 3? = 20 ?
2. Perimeter = 2? + 4? + 5? = 11 ?
3. Perimeter = 3?? + 6?? + 4?? + 5?? + 5 ?? + 4?? = 27 ??

Circumference of a Circle

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

1. diameter 9 ??
2. radius 3½?
3. diameter 4.5 ??
4. 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 ??

Areas of Rectangles and Triangles

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, ?

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, 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

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 30 ?. What is its area?

Solution

Given circumference, ? = 30 ?

C = 2??