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

TOPIC 11: PERIMETERS AND AREAS ~ MATHEMATICS FORM 1

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BASIC MATHEMATICS FORM ONE FULL NOTES PERIMETERS AND AREAS COORDINATE OF A POINT PROFIT AND LOSS NUMBERS GEOMETRY Approximations UNITS DECIMAL AND PERCENTAGEFRACTIONS TOPIC 1: NUMBERS ~ MATHEMATICS FORM 1

TOPIC 11: PERIMETERS AND AREASΒ 

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 inβ€‹β€‹Β π‘šβ€‹β€‹Β ,β€‹β€‹Β π‘π‘šβ€‹β€‹Β ,π‘‘π‘šβ€‹β€‹Β ,π‘š,π‘˜π‘šβ€‹β€‹Β e. t. c

Examples

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_13.57.51_1465469917550.Png

Example 1

Find the perimeters of the following shapes

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_14.01.29_1465470127574.Png

Solution

Perimeter = 7π‘šβ€‹β€‹Β + 7π‘šβ€‹β€‹Β + 3π‘šβ€‹β€‹Β + 3π‘šβ€‹β€‹Β = 20β€‹β€‹Β π‘š

Perimeter = 2π‘šβ€‹β€‹Β + 4π‘šβ€‹β€‹Β + 5π‘šβ€‹β€‹Β = 11β€‹β€‹Β π‘š

Perimeter = 3π‘π‘šβ€‹β€‹Β + 6π‘π‘šβ€‹β€‹Β + 4π‘π‘šβ€‹β€‹Β + 5π‘π‘šβ€‹β€‹Β + 5β€‹β€‹Β π‘π‘šβ€‹β€‹Β + 4π‘π‘šβ€‹β€‹Β = 27β€‹β€‹Β π‘π‘š

Circumference of a Circle

The Value of Pi ( Ξ )

Estimate the value of Pi ( Ξ )

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

The perimeter of a circle is the length of its circumference​​ 𝑖.β€‹β€‹Β π‘’β€‹β€‹Β π‘π‘’π‘Ÿπ‘–π‘šπ‘’π‘‘π‘’π‘Ÿβ€‹β€‹Β =β€‹β€‹Β π‘π‘–π‘Ÿπ‘π‘’π‘šπ‘“π‘’π‘Ÿπ‘’π‘›π‘π‘’. Experiments show that the ratio of the circumference to the diameter is the same for all circles

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_14.05.36_1465470386147.Png

The Circumference of a Circle

Calculate the circumference of a circle

Example 2

Find the circumferences of the circles with the following measurements. Takeβ€‹β€‹Β πœ‹β€‹β€‹Β = 3.14

diameter 9β€‹β€‹Β π‘π‘š

radius 3Β½π‘š

diameter 4.5β€‹β€‹Β π‘‘π‘š

radius 8β€‹β€‹Β π‘˜π‘š

Solution

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_14.22.41_1465471403119.Png

Example 3

The circumference of a car wheel is 150β€‹β€‹Β π‘π‘š. What is the radius of the wheel?

  Past Papers Basic Mathematics Form Two

Solution

Given circumference,​​ 𝐢​​ = 150β€‹β€‹Β π‘π‘š

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_14.38.06_1465472345202.Png

βˆ΄β€‹β€‹Β The radius of the wheel is 23.89β€‹β€‹Β π‘π‘š

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​​ 𝑀

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_14.45.05_1465472738063.Png

Consider a square of side​​ 𝑙

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_14.48.41_1465472998064.Png

Consider a triangle with a height,β€‹β€‹Β β„Žβ€‹β€‹Β and a base,​​ 𝑏

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_14.51.18_1465473127035.Png

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:

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_14.56.06_1465473454530.Png

The Area of a Trapezium

Calculate the area of a trapezium

Consider a trapezium of height,β€‹β€‹Β β„Žβ€‹β€‹Β and parallel sidesβ€‹β€‹Β π‘Žβ€‹β€‹Β and​​ 𝑏

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_14.53.31_1465473310003.Png

Example 4

The area of a trapezium is120β€‹β€‹Β π‘š!. Its height is 10β€‹β€‹Β π‘šβ€‹β€‹Β and one of the parallel sides is 4β€‹β€‹Β π‘š. What is the other parallel side?

Solution

Given area,​​ 𝐴​​ = 120β€‹β€‹Β π‘š2, height,β€‹β€‹Β β„Žβ€‹β€‹Β = 10β€‹β€‹Β π‘š, one parallel side,β€‹β€‹Β π‘Žβ€‹β€‹Β = 4β€‹β€‹Β π‘š. Let other parallel side be,​​ 𝑏

Then

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_15.16.05_1465474596177.Png

Area of a Circle

Areas of Circle

Calculate areas of circle

Consider a circle of radius r;

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_15.00.56_1465473688041.Png

Example 5

Find the areas of the following figures

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_15.06.15_1465474008600.Png

Solution

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_15.10.24_1465474258267.Png

Example 6

A circle has a circumference of 30β€‹β€‹Β π‘š. What is its area?

Solution

Given circumference,​​ 𝐢​​ = 30β€‹β€‹Β π‘š

C = 2πœ‹π‘Ÿ

Https://Sdimg.blob.core.windows.net/Images/Shuledirect/22472/Original/Screen_Shot_2016-06-09_At_15.13.11_1465474424623.Png

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