Mathematics Notes

MATHEMATICS FORM 1 – PERIMETERS AND AREA

msomimaktaba, November 11, 2018August 17, 2024

PERIMETERS AND AREA

PERIMETER:

The perimeter is the length of a closed curve. It is measured in centimeters, meter, kilometer etc

To find the perimeter of a shape, add the length of the sides which enclose it.

Example:

Find the perimeter of rectangle which is 6m by 9m

solution

Consider the diagram below

There are two lengths of 6m, and two of 9m
Add these 6m + 6m + 9m + 9m = 30m
The perimeter is 30m

2. find the perimeter of the following shapes

Solution
(a)The Perimeter = 4m +6m +10m +12m

=32m

The perimeter is 32m

(b) For the triangle

The perimeter = 4cm + 5cm +7cm

= 16cm

The perimeter = 16cm

(a) In the figure below find the value of p if the perimeter is 24cm

solution.

The perimeter = 5cm +6cm +P cm +P cm

24 =16cm +2Pcm

2Pcm = 24cm – 16cm

2Pcm = 8cm

P = 4

Circumference of circles:

The perimeter of a circle is the length of its circumference.

If c is the circumference, d is the diameter, then the result is

Multiplying across by d, it become d

If radius r is given, then

NOTE:

Example

1) A Circular running track has radius 6cm. What is the length of the track?

Solution

Take

C=2x 3.14×6

C=37.68cm

(a) Circumference 88m

(b) Circumference 210m

Solution:

28m

The diameter d = 28m

AREA:-

The area of a shape is the one that gives how much surface it covers.

Area is measured in square centimeters (cm)², square meters (m)², and square kilometer (km)²……….

Rectangle:-
consider the figure below

Area = length x width

= a units x b units

= ab units square

Example:

The length of a rectangle is 55cm, and the length is 8cm. What is the area?.

Solution:

Area = length x width

= 55cm x 8cm

= 440cm²

The area of a rectangle = 440cm²
2. The area of a rectangle is 2470m², and the length is 65m, what is the width .

Solution

Given Area = 2470m²

Length = 65m

But Area = length x width

2470m² = 65m x width

Width = 38m

The width of the rectangle is 38m.

Parallelogram

The area of a parallelogram = base x height

If base is b and height is h

Then Area = bh

The height of parallelogram is the perpendicular height.

Example
The parallelogram has base 15cm and height 22mm.What is its area? give your answer in cm

Height = 22mm

10cm = 10mm

? = 22mm

= 2.2 cm

But Area = base x height

= 15cm x 2.2 cm

= 33cm²

The area of a parallelogram = 33cm²

2. A rhombus has side 1.2m and height 0.8m. What are its areas?

Solution

But Area = base x height

=1.2m x 0.8m

= 0.96m²

The area of a rhombus = 0.96m²

Triangle:-

Consider the triangle below:-

Example:
find area of triangle of below

9m²
The area = 9m²

TRAPEZIUM
consider the parallel side of a trapezium are a and b as shown below

Then

Example; Find the area of the Trapezium below

Solution

Where b = 20cm + 6cm

b = 26cm

a = 20cm

h = unknown

Area =184cm²

Area of a circle:-

Consider a circle with radius r shown below

If the circle has the diameter d as shown below

Then its area is

Since, d = r x r
d = 2r

Example:-

Find the area of the circle with the following measurement

(a) Diameter 8m

(b) Radius 3cm

(c) Diameter 0.2km

Solution

EXERCISE
1. find the perimeter of the shapes

2. find the area of these shapes

3. A ball of radius 5m rolls along the ground 100 times ,

a) How far has it traveled?

b) How many times must the ball roll for it to cover 157m?

(Take =3.14)

SOLUTIONS TO EXERCISE 1
1. a) Perimeter = 2.5cm + 8cm + 10cm + 3cm

Perimeter = 23.5cm

b) Perimeter of triangle = 8cm + 6cm +5cm

Perimeter = 19cm

c) Perimeter =2 (12cm + 7cm)

= 2 x 19cm

Perimeter = 38cm

2. a) Area = base x height

Base = 2m, height = 1.5m

Area = 2m x 1.5m

= 3.0m²

Area = 3m²

Area = 6m²

a) It Rolls 100 times.

Rolling 1 time cover 31.4m

Rolling 100 times it will cover 31.4m x 100

= 3140m

It will cover 3140m

b) For the ball to cover 157m, it will roll x times

x= 5

The ball will rolls 5 times.

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