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 𝑚𝑚 , 𝑐𝑚 ,𝑑𝑚 ,𝑚,𝑘𝑚 e. t. c

Examples

Example 1

Find the perimeters of the following shapes

Solution

1. Perimeter = 7𝑚 + 7𝑚 + 3𝑚 + 3𝑚 = 20 𝑚
2. Perimeter = 2𝑚 + 4𝑚 + 5𝑚 = 11 𝑚
3. 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

1. diameter 9 𝑐𝑚
2. radius 3½𝑚
3. diameter 4.5 𝑑𝑚
4. 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

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