Area and Perimeters

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

Find the perimeters of triangles and quadrilaterals

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 as 3.14159. 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

Calculate the circumference of a circle

1. diameter 9 𝑐𝑚
2. radius 3½𝑚
3. diameter 4.5 𝑑𝑚
4. radius 8 𝑘𝑚

Solution

Example

Calculate the circumference of a circle

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

Calculate the area of a trapezium

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

Calculate areas of circle

Solution

Example

Calculate areas of circle

Solution

Given circumference, 𝐶 = 30 𝑚

C = 2𝜋𝑟

Exercise

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2. Find the area of a circle with diameter 35 cm.( use Π = 22/7)

3. Calculate the area of a trapezium with parallel sides 3 cm and 5 cm and distance between them is 12 cm.

4. Find the height of a triangle with base 50 cm and area 300 cm2.

5. Find the area of a circle of diameter 40 cm. ( given π=3.14).