TOPIC 11: PERIMETERS AND AREAS ~ MATHEMATICS FORM 1

TOPIC 11: PERIMETERS AND AREAS 

Perimeters of Triangles and Quadrilaterals

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​​ 𝑚​​ ,​​ 𝑐𝑚​​ ,𝑑𝑚​​ ,𝑚,𝑘𝑚​​ e. t. c

Examples

Example 1

Find the perimeters of the following shapes

Solution

Perimeter = 7𝑚​​ + 7𝑚​​ + 3𝑚​​ + 3𝑚​​ = 20​​ 𝑚

Perimeter = 2𝑚​​ + 4𝑚​​ + 5𝑚​​ = 11​​ 𝑚

Perimeter = 3𝑐𝑚​​ + 6𝑐𝑚​​ + 4𝑐𝑚​​ + 5𝑐𝑚​​ + 5​​ 𝑐𝑚​​ + 4𝑐𝑚​​ = 27​​ 𝑐𝑚

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​​ 𝑖.​​ 𝑒​​ 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟​​ =​​ 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​​ 𝜋​​ = 3.14

diameter 9​​ 𝑐𝑚

radius 3½𝑚

diameter 4.5​​ 𝑑𝑚

radius 8​​ 𝑘𝑚

Solution

Example 3

The circumference of a car wheel is 150​​ 𝑐𝑚. What is the radius of the wheel?

Solution

Given circumference,​​ 𝐶​​ = 150​​ 𝑐𝑚

∴​​ The radius of the wheel is 23.89​​ 𝑐𝑚

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​​ 𝑙​​ and width​​ 𝑤

Consider a square of side​​ 𝑙

Consider a triangle with a height,​​ ℎ​​ and a base,​​ 𝑏

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​​ 𝑎​​ and​​ 𝑏

Example 4

The area of a trapezium is120​​ 𝑚!. Its height is 10​​ 𝑚​​ and one of the parallel sides is 4​​ 𝑚. What is the other parallel side?

Solution

Given area,​​ 𝐴​​ = 120​​ 𝑚2, height,​​ ℎ​​ = 10​​ 𝑚, one parallel side,​​ 𝑎​​ = 4​​ 𝑚. Let other parallel side be,​​ 𝑏

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​​ 𝑚. What is its area?

Solution

Given circumference,​​ 𝐶​​ = 30​​ 𝑚

C = 2𝜋𝑟