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AREA OF PATHS AND VERANDAHS
    Area of verandah is nothing but the difference between the areas of two rectangles.
    Illustration 4    
        A rectangular field is 45 m × 30 m. A path 1.5 m wide is to be constructed along the sides inside the field. Find the area of the path and its cost of construction at the rate of Rs 1.50 per square metre. 
    Solution    
        Length of the field = 45 m                                                
        Width of the field = 30 m 
        Area of the field  = 45 × 30 sq m = 1350 sq m                
        Length of the inner rectangle = 45 – 3 or 42 m 
        Width of the inner rectangle = 30 – 3 or 27 m
        Area of the inner rectangle = 42 × 27 sq m = 1134 sq m
        Area of path = 1350 – 1134 or 216 sq m 
        Cost of constructing 1 sq m of path = Rs 1.50 
        Cost of constructing 216 sq m of path = Rs 1.50 × 216 = Rs 324

Area of Cross Roads
    ABCD is a rectangular piece of ground. Two roads one parallel to the length and the other parallel to the breadth together are called cross roads.

Illustration 5     
        A field is 75 m long and 32 m wide. Two 3 m wide roads are constructed in the centre of the field one parallel to its length and the other parallel to its breadth. Find (a) area of cross roads (B) the cost of levelling the roads at Rs 1.80 per square metre (C)        area of the remaining field.

Solution 

(A)     Area of the road parallel to the length = 75 × 3 m2 = 225 m2 
        Area of the road parallel to the breadth = 32 × 3 m2  = 96 m2 
        Area of shaded portion     = 3 × 3 or 9 m2
             Area of the roads = (225 + 96 – 9) m2 = 312 m
 (B)    Cost of levelling 1 m2 road = Rs 1.80
        Cost of levelling 312 m2 road = Rs 312 × 1.80 = Rs 561.60
(C)       Area of field = 75 × 32 or 2400 m2
        Area of remaining field = (2400 – 312) m2 = 2088 m2

 

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