Area of Path and Verandah


 
 
Concept Explanation
 

Area of Path and Verandah

Area of Path & Verandah: 

 It is observed that in square or rectangular gardens or parks. Some space in the form of path is left inside or outside or in between as cross paths.

Illustration: A footpath of uniform width 5 m runs round the inside of a rectangular park 38 m long and 32 m wide. Find the area of the path.

Solution: Let ABCD be the rectangular park and PQRS be the internal boundaries of the path.

We have, Length AB= 38 m and Breadth BC= 32 m:

Thus, Area of rectangle ABCD = AB large times BC = 38 m large times 32 m = 1216 large ^{m^{2}}

Now, Length PQ  = 38 m - 5 m - 5 m = 28 m and Breadth QR = 32 m - 5 m - 5 m = 22m

Area of rectangle PQRS = PQ large times RS = 28 m large times 22 m = 616 large ^{m^{2}}

Area of footpath = Area of rectangle ABCD - Area of rectangle PQRS = 1216 - 616=600 large ^{m^{2}}

Thus, Area of footpath =600 large ^{m^{2}}

The area of the crossroads = Area of the two colored rectangles - Area of the red colored rectangle at the centre.

We are subtracting the area of the rectangle because we are taking it into consideration two times.

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Sample Questions
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Question : 1

 A rectangular lawn is 15 m by 40 m .It has two roads each 4 m wide running in the middle of it, one parallel to the length and the other parallel to the breadth . Find the area of the roads.

Right Option : A
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Explanation
Question : 2

A square lawn is surrounded by a path 3 m wide. If the area of the path is 360 sq m. Find the area of the lawn.

Right Option : A
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Explanation
Question : 3

A floor is 15 m long and 9 m wide. A square carpet of side 5 m is laid on the floor. Find the area of the floor not carpeted ?

Right Option : D
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Explanation
 
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