2. Area of Rectangle and Regular Shapes

Perimeter
    The perimeter of a closed figure is the length of the boundary of the figure.
    The idea of perimeter is widely used in our daily life.

•          A farmer who wants to fence his field.
•          An engineer who plans to build a compound wall on all sides of a house.
•          A person preparing a track to conduct sports.

    All these people use the idea of ‘perimeter’.

1.    Perimeter of Rectangle:  The perimeter of a rectangle is the sum of all its sides. The opposite sides of rectangle are equal. If one side is l unit and the other side is b unit, then 

2 .    Perimeter of a square: All four sides of a square are equal. If one side of a square measures 'a' unit, we can say that both the length and the breadth are a unit each.    

     The perimeter of a square is equal to four times the length of its sides.

3.    Perimeter of a triangle :

Perimeter = AB + BC + CA = a + b + c

Note: In general, if the sides of a polygon are equal, that is, if it is a regular polygon, its perimeter will be the product of the length of its side with the number of sides.
        The perimeter of a regular pentagon = 5a units 
        The perimeter of a regular hexagon = 6a units
        The perimeter of a regular octagon = 8a units 
        where a is the length of one side.

Ex.1     Pinky runs around a square field of side 75 m, Bob runs around a rectangular field with a length of 160 m and breadth of 105 m. Who covers more distance and by how much?

Sol.:     Distance covered by Pinky in one round = Perimeter of the square 
                              = 4 × length of a side
                              = 4 × 75 m = 300 m
        Distance covered by Bob in one round     = Perimeter of the rectangle
                        = 2 × (length + breadth)
                        = 2 × (160 m + 105 m)
                        = 2 × 265 m = 530 m
        Difference in the distance covered = 530 m – 300 m = 230 m.
        Therefore, Bob covers more distance by 230 m.

Ex.2    Find the perimeter of a regular pentagon with each side measuring 3 cm.
Sol.:     This regular closed figure has 5 sides, each with a length of 3 cm.
        Thus, we get 
        Perimeter of the regular pentagon = 5 × 3 cm = 15 cm

Ex.3     A piece of string is 48 cm long. What will be the lenght of each side if the string is used to form:
        (i) a square             (ii) an equilateral triangle      (iii) an regular octagon .
Sol.  (i)     one side of  the square  = Perimeter ¸ 4 = 48 ¸ 4  = 12 cm      
        (ii)     one side of  the equilateral triangle  = Perimeter ¸  3 = 48 ¸ 3  = 16 cm      
        (iii)     one side of regular octagon = Perimeter ¸ 8 = 48 ¸ 8  = 6 cm