# Area of a rectangular paths

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### 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.