Area of a rectangular path. : Area of a rectangular path. BY
V JOIS
TGT(Maths)
K.V.No.1 Mangalore.
Area of a rectangle=length x breadthArea of a square=side x side : Area of a rectangle=length x breadthArea of a square=side x side Rectangular paths are generally found around (outside or inside) a rectangle or in the form of central paths.
Finding area of paths. : Finding area of paths. Example:A garden is 90m long and 75m broad.A path 5m wide is to be built outside around it.Find the area of the path.
Solution:Let us represent the garden by the rectangle PQRS and the path around it by the shaded region.
Slide 4: A B C D P Q R S 100M 90M 75M 85M Now AB=DC=(90+5+5)M=100M
AD=BC=(75+5+5)M=85M
Area of the path=Area of the rectangle ABCD- Area of the rectangle PQRS=100 X 85-90 X75 Sq m=(8500- 6750)Sq m=1750sq m : Area of the path=Area of the rectangle ABCD- Area of the rectangle PQRS=100 X 85-90 X75 Sq m=(8500- 6750)Sq m=1750sq m Thus, the area of the path is 1750sq m
Example:Two cross roads each of width 5m run at right angles through the centre of a rectangular park of length 700m and breadth 300m parallel to its sides.Find the area of the roads.Also,find the cost of constructing roads at the rate of Rs105 per sq.m . : Example:Two cross roads each of width 5m run at right angles through the centre of a rectangular park of length 700m and breadth 300m parallel to its sides.Find the area of the roads.Also,find the cost of constructing roads at the rate of Rs105 per sq.m . Solution:Let us represent the rectangular park by the rectangle ABCD and the two cross roads by the rectangles EFGH and PQRS.
Slide 7: A B C D F G H L M N O 5M 5M 700M 300M P Q R S E
Now,Area of the roads=Area of EFGH+ Area of PQRS-Area of LMNO=(300X5+700X5-5X5)Sq m=(1500+3500-25)Sq m=4975 Sq m : Now,Area of the roads=Area of EFGH+ Area of PQRS-Area of LMNO=(300X5+700X5-5X5)Sq m=(1500+3500-25)Sq m=4975 Sq m Cost of constructing roads at the rate of Rs105 per Sq m=Rs4975x105
=Rs522375.
Work out the following problems : Work out the following problems 1. A path 5m wide runs along inside a square park of side 100m. Find the area of the path.