TOPIC 11: PERIMETERS AND AREAS ~ MATHEMATICS FORM 1

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

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