Topic 11: Perimeters And Areas - Mathematics Form One


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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 𝑚 , 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


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



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 4


The area of a trapezium is120 𝑚!. Its height is 10 𝑚 and one of the parallel sides is 4 𝑚. What is the other parallel side?


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


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 𝑚. What is its area?


Solution


Given circumference, 𝐶 = 30 𝑚


C = 2𝜋𝑟



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