BASIC MATHEMATICS FORM ONE-Topic 11: PERIMETERS AND AREAS

 Perimeters of Triangles and QuadrilateralsThe Perimeters of Triangles and QuadrilateralsFind the perimeters of triangles and quadrilateralsPerimeter
– 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 ?? , ?? ,?? ,?,?? e. t. cExamples

Example 1Find the perimeters of the following shapes

Solution

1. Perimeter = 7? + 7? + 3? + 3? = 20 ?
2. Perimeter = 2? + 4? + 5? = 11 ?
3. Perimeter = 3?? + 6?? + 4?? + 5?? + 5 ?? + 4?? = 27 ??

Circumference of a CircleThe 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 ?. ?
????????? = ?????????????. Experiments show that
the ratio of the circumference to the diameter is the same for all
circles

The Circumference of a CircleCalculate the circumference of a circleExample 2Find the circumferences of the circles with the following measurements. Take ? = 3.14

1. diameter 9 ??
2. radius 3½?
3. diameter 4.5 ??
4. radius 8 ??

Solution

Example 3The circumference of a car wheel is 150 ??. What is the radius of the wheel?SolutionGiven circumference, ? = 150 ??

∴ The radius of the wheel is 23.89 ??Areas of Rectangles and TrianglesThe Area of a RectangleCalculate the area of a rectangleArea
– 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. cConsider a rectangle of length ? and width ?

Consider a square of side ?

Consider a triangle with a height, ℎ and a base, ?

Areas of Trapezium and ParallelogramThe Area of a ParallelogramCalculate area of a parallelogramA parallelogram consists of two triangles inside. Consider the figure below:

The Area of a TrapeziumCalculate the area of a trapeziumConsider a trapezium of height, ℎ and parallel sides ? and ?

Example 4The area of a trapezium is120 ?!. Its height is 10 ? and one of the parallel sides is 4 ?. What is the other parallel side?SolutionGiven area, ? = 120 ?², height, ℎ = 10 ?, one parallel side, ? = 4 ?. Let other parallel side be, ?Then

Area of a CircleAreas of CircleCalculate areas of circleConsider a circle of radius r;

Example 5Find the areas of the following figures

Solution

Example 6A circle has a circumference of 30 ?. What is its area?SolutionGiven circumference, ? = 30 ?C = 2??