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

TOPIC 11: PERIMETERS AND AREAS ~ MATHEMATICS FORM 1

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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 π‘šπ‘š , π‘π‘š ,π‘‘π‘š ,π‘š,π‘˜π‘š e. t. c
Examples
Example 1
Find the perimeters of the following shapes
Solution
  1. Perimeter = 7π‘š + 7π‘š + 3π‘š + 3π‘š = 20 π‘š
  2. Perimeter = 2π‘š + 4π‘š + 5π‘š = 11 π‘š
  3. Perimeter = 3π‘π‘š + 6π‘π‘š + 4π‘π‘š + 5π‘π‘š + 5 π‘π‘š + 4π‘π‘š = 27 π‘π‘š

 

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. 𝑒 π‘π‘’π‘Ÿπ‘–π‘šπ‘’π‘‘π‘’π‘Ÿ = 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
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œ‹ = 3.14
  1. diameter 9 π‘π‘š
  2. radius 3Β½π‘š
  3. diameter 4.5 π‘‘π‘š
  4. radius 8 π‘˜π‘š
Solution
Example 3
The circumference of a car wheel is 150 π‘π‘š. What is the radius of the wheel?
Solution
Given circumference, 𝐢 = 150 π‘π‘š
∴ The radius of the wheel is 23.89 π‘π‘š
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
Consider a square of side 𝑙
Consider a triangle with a height, β„Ž and a base, 𝑏
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, β„Ž and parallel sides π‘Ž and 𝑏
Example 4
The area of a trapezium is120 π‘š!. Its height is 10 π‘š and one of the parallel sides is 4 π‘š. What is the other parallel side?
Solution
Given area, 𝐴 = 120 π‘š2, height, β„Ž = 10 π‘š, one parallel side, π‘Ž = 4 π‘š. Let other parallel side be, 𝑏
Then

 

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 30 π‘š. What is its area?
Solution
Given circumference, 𝐢 = 30 π‘š
C = 2πœ‹π‘Ÿ

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