Introduction
    In this chapter we learn about the perimeter and area of a rectangle and a square and circumference (perimeter) of a circle and area of a triangle, a parallelogram and a circle etc.

PERIMETER and area
1.    Perimeter
    The perimeter of a plane figure is the length of its boundary. The units of perimeter are the same as the units of length, i.e., cm, m, etc.
    
2.    Area
    The measurement of the region enclosed by a plane figure is called its area.
    
3.    STANDARD UNITS OF AREA
    The units of area are sq cm (written as cm2), sq metres (written as m2), etc. 
    Conversion of units
    Length units            Area units
    1 cm = 10 mm         1 cm2 = (10 × 10) mm2 = 100 mm2    
    1 dm = 10 cm         1 dm2 = (10 × 10) cm2 = 100 cm2    
    1 m = 10 dm          1 m2 = (10 × 10) dm2 = 100 dm2    
    1 m = 100 cm        1 m2 = (100 × 100) cm2 = 10000 cm2    
                                  1 hectare = 10000 m2    

4.    AREA  AND PERIMETER OF A RECTANGLE
    Consider a rectangle with length = l units and breadth = b units. Then, we have :
    (i)     Area of the rectangle = (l × b) sq units

Illustration 1     
        A door of length 1 m and breadth 0.5 m is on a wall. The length of the wall is 4.5 m and the breadth is 3.6 m as shown in Fig. Find the cost of white washing the wall, if the rate of white washing the wall is Rs 20 per m2. 

Solution
        We have,                                             
        l = Length of the wall = 4.5 m, 
        b = Breadth of the wall = 3.6 m
    ∴    Area of the wall = l × b = 4.5 m × 3.6 m = 16.2 m2 
          Area of the door = 1 m × 0.5 m = 0.5 m2 
    ∴   Area to be white washed = 16.2 m2 – 0.5 m2 = 15.7 m2 
        Cost of white washing the wall = Rs (15.7 × 20) = Rs 314

Illustration 2    
        The length and breadth of a playground are 75 m 20 cm and 34 m 80 cm, respectively. Find the cost of levelling it at Rs 1.50 per square metre. How long will a boy take to go three times round the field, if he walks at the rate of 1.5 m/sec.

Solution        
         We have,
        Length of the playground  = 75 m 20 cm = 75.20 cm 
        Breadth of the playground  = 34 m 80 cm = 34.80 m .
    ∴    Area of the playground      = 75.20 × 34.80 m2 = 2616.96 m2 
   ∴   Cost of levelling = Rs 2616.96 × 1.50 = Rs 3925.44 
        Perimeter of the playground  = 2 (Length + Breadth) 
            = 2 (75.20 + 34.80) m = 2 × 110m = 220m 

Illustration 3    
        A room is 9 m long, 8 m broad and 6.5 m high. It has one door of dimensions 2 m ´ 1.5 m and three windows each of dimensions 1.5 m × 1 m. Find the cost of white washing the walls at Rs 3.80 per square metre.
  Solution             
        The dimensions of the room are:
        l = Length = 9 m, b = Breadth = 8 m and h = Height = 6.5 m
  ∴       Area of 4 walls of the room = 2 {(l + b) × h} = 2 {9 + 8) × 6.5}m2 =221m2 
             Area of 1 door = (2 × 1.5) m2 =3 m2
             Area of 3 windows = {3 × (1.5 × l)}m2 = 4.5 m2
   ∴     Area to be white washed = Area of 4 walls – Area of 1 door –  Area of 3 windows
                       = (221 –3 – 4.5)m2 =213.5m2 
    So, cost of white washing = Rs (213.5 × 3.80) = Rs 811.30