LENGTH (PERIMETERS OF REGULAR AND IRREGULAR SHAPES)

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Perimeter simply means addition of all the sides of a given plane shape. Plane shapes can be classified into two types:

  1. Regular shapes.
  2. Irregular shapes.

PERIMETERS OF REGULAR PLANE SHAPES

The regular plane shapes are as follows:

  1. Square
  2. Rectangle
  3. Triangle
  4. Circle
  5. Kite
  6. Trapezium
  7. Rhombus
  8. Parallelogram

 

Example 1

Find the perimeter of the rectangle below:

                    7cm

5cm

 

 

 

 

Solution

Perimeter = sum of all sides     OR      2L + 2B

The shape has four sides.                     2(7) + 2(5)

Perimeter = 7 + 7 + 5 + 5                     14 + 10

Perimeter = 24cm                                 24cm

Example 2

Find the perimeter of the square below:

           5cm

 

 

 

 

Solution

A square has four sides that are all equal

Perimeter = sum of all sides        OR     4 Lenght

Perimeter = 5 + 5 + 5 + 5                       4  5

Perimeters = 20cm                                 20cm

Example 3

Find the perimeter of the shape below:

Solution

The shape (a trapezium) has four sides.

Perimeter = sum of all sides

Perimeter = 80 + 50 + 100 + 110

Perimeter = 340m

PERIMETER OF IRREGULAR PLANE SHAPES

Example 1. Find the perimeter of the shape below:

Solution

The shape has 5 sides.

Perimeter = sum of all sides

Perimeter = 5 + 4 + 4 + 4 + 3

Perimeter = 20in

Example 2.  Find the perimeter of the shape below:

Solution

The shape has six sides. First find the missing sides

There are 3 missing sides, the first one is 5m, the second one is 7m and the third one is ( 5 + 11 = 16m )

Perimeters = (7 +5) + 5 + 5 + 11 + 7 + 16

Perimeters = 56m

Circumference of a Circle

The distance around a rectangle or a square is as you might remember called the perimeter. The distance around a circle on the other hand is called the circumference (c). Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of a circle defines the region occupied by it.

 

A line that is drawn straight through the midpoint of a circle and that has its end points on the circle border is called the diameter (d)

Half of the diameter, or the distance from the midpoint to the circle border, is called the radius of the circle (r).

The circumference of a circle is found using this formula:

Circumference (or) perimeter of a circle = 2πR  or C=πd where,

R is the radius of the circle

π is the mathematical constant with an approximate (up to two decimal points) value of 3.14

Pi (π) is a special mathematical constant; it is the ratio of circumference to diameter of any circle.

where C = π D

C is the circumference of the circle

D is the diameter of the circle

For example: If the radius of the circle is 4cm then find its circumference.

Given: Radius = 4cm

Circumference = 2πr

= 2 x 3.14 x 4

= 25.12 cm

Examples

Question 1: What is the circumference of the circle with diameter 4 cm?

Solution:

Since the diameter is known to us, we can calculate the radius of the circle,

Therefore, Circumference of the Circle = 2 x 3.14 x 2 = 12.56 cm.

Question 2: Find the radius of the circle having C =  50 cm.

Solution: 

Circumference = 50 cm

As per formula,  C = 2 π  r

This implies, 50 = 2 π  r

50/2 = 2 π  r/2

25 = π  r

or r =  25/π

Therefore, the radius of the circle is 25/π  cm.

 

AREAS OF PLANE SHAPES

Area is measured in square units. The area of regular plane shapes is given in the table below;

Examples: find the area of the rectangle below:

Solution

Area of rectangle = length  bredth

Area of rectangle = 9  4

Area of rectangle = 36m2

Example 2: find the area of the shape below:

Solution

The shape above is a trapezium.

Area of a trapezium =

Area of trapezium =   (6 + 8) 4

Area of trapezium =   14 4

Area of trapezium =

Area of trapezium =

Area of trapezium = 28

Example 3: find the area of the shape below:

Solution

The shape is a square.

Area of a square = length  length

Area of square = 8  8

Area of square = 64cm2

Examples 4: find the area of the shape below:

Solution

The shape is a circle. = 3.14 or 22/7

Area of a circle =

Area of circle = 3.14  2  2

Area of circle = 12.56cm2

Example 5: find the area of the shape below:

Solution

The shape is a triangle.

Area of a triangle =   base of triangle  height of triangle

Area of triangle =   11  10

Area of triangle =

Area of triangle =

Area of triangle = 55cm2

AREA OF IRREGULAR PLANE SHAPES

When finding the areas of irregular plane shapes, split the irregular plane shape in regular plane shapes. Find their areas and sum them all together.      

Example: find the area of the shape below:

Solution

The shape can be split into two regular plane shapes A and B

A = a rectangle with length 8m and breadth 4m

B = a square with length 10m

Area of A = 8  4

Area of A = 32m2

Area of B = 10 10

Area of B = 100m2

Area of the irregular plane shape = 32 + 100

Area of the irregular plane shape = 132m2

AREA OF SHADED PORTIONS

Example: find the area of the shaded portion in the figure below:

Solution

The shaded portion is between a rectangle (the bigger shape) and a square (the smaller shape)

Area of the rectangle = length  breadth

Area of rectangle = 20

Area of rectangle = 300cm2

Area of the square = length  length

Area of square = 8  8

Area of square = 64cm2

Area of shaded portion = area of rectangle – area of square

Area of shaded portion = 300 – 64

Area of shaded portion = 236cm2

Area of Complex figures

 

A complex figure is made up of two or more shapes. To find the area of a complex figure, break the figure into smaller parts.

 

 

 

 

 

 

Example 6: Find the area of the swimming pool at Dew’s hotel.

 

Solution:

Step 1: Break up the figure into smaller parts. Look for rectangles and squares.

 

 

Step 2: Find the area of each part.

Square                                                            

Area = side x side

A  = 10m x 10m

A = 100 square meters.

 

 

 

 

Rectangles                                  

               

  A = length x width

A = 12m x 6m

A = 72 square meters

Step 3: Add the areas.

The area is 72 + 100 = 172 square meters.

 

Quiz

  1. Find the perimeter of the following shapes:

 

 

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