Home MATHEMATICS TOPIC 11: PERIMETERS AND AREAS ~ MATHEMATICS FORM 1

# TOPIC 11: PERIMETERS AND AREAS ~ MATHEMATICS FORM 1

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## TOPIC 11: PERIMETERS AND AREASย

The Perimeters of Triangles and Quadrilaterals

Find the perimeters of triangles and quadrilaterals

Perimeter โ 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 inโโย ๐โโย ,โโย ๐๐โโย ,๐๐โโย ,๐,๐๐โโย e. t. c

Examples

Example 1

Find the perimeters of the following shapes

Solution

Perimeter = 7๐โโย + 7๐โโย + 3๐โโย + 3๐โโย = 20โโย ๐

Perimeter = 2๐โโย + 4๐โโย + 5๐โโย = 11โโย ๐

Perimeter = 3๐๐โโย + 6๐๐โโย + 4๐๐โโย + 5๐๐โโย + 5โโย ๐๐โโย + 4๐๐โโย = 27โโย ๐๐

#### Circumference of a Circle

The Value of Pi ( ฮ )

Estimate the value of Pi ( ฮ )

The number ฯ 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 “ฯ” since the mid 18th century, though it is also sometimes spelled out as “pi” (/paษช/).

The perimeter of a circle is the length of its circumferenceโโย ๐.โโย ๐โโย ๐๐๐๐๐๐๐ก๐๐โโย =โโย ๐๐๐๐๐ข๐๐๐๐๐๐๐๐. 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. Takeโโย ๐โโย = 3.14

diameter 9โโย ๐๐

diameter 4.5โโย ๐๐

Solution

Example 3

The circumference of a car wheel is 150โโย ๐๐. What is the radius of the wheel?

Past Papers Basic Mathematics Form Two

Solution

Given circumference,โโย ๐ถโโย = 150โโย ๐๐

โดโโย The radius of the wheel is 23.89โโย ๐๐

#### The Area of a Rectangle

Calculate the area of a rectangle

Area โ 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 lengthโโย ๐โโย and widthโโย ๐ค

Consider a square of sideโโย ๐

Consider a triangle with a height,โโย โโโย and a base,โโย ๐

#### 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,โโย โโโย and parallel sidesโโย ๐โโย andโโย ๐

Example 4

The area of a trapezium is120โโย ๐!. Its height is 10โโย ๐โโย and one of the parallel sides is 4โโย ๐. What is the other parallel side?

Solution

Given area,โโย ๐ดโโย = 120โโย ๐2, height,โโย โโโย = 10โโย ๐, one parallel side,โโย ๐โโย = 4โโย ๐. Let other parallel side be,โโย ๐

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 30โโย ๐. What is its area?

Solution

Given circumference,โโย ๐ถโโย = 30โโย ๐

C = 2๐๐