A school playground is divided by a 2 m wide path, which is parallel to the width of the playground and a 3 m wide path which is parallel to the length of the ground as given in the figure below. If the length and width of the playground are 120 m and 80 m respectively, find the area of the remaining playground.

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Solution

Given, dimensions of playground $= 120 m \times 80 m$

$∵$ Area of rectangle $A B C D = 120 \times 80 = 9600 m^{2}$
Area of rectangle $G H I J = J I \times I H = 2 \times 77 = 154 m^{2}$

Area of rectangle $A B F E = B F \times A B = 3 \times 120 = 360 m^{2}$
$∴$ Area of remaining playground = Area of rectangle ABCD - Area of rectangle ABFE - Area of GHIJ
$= 9600 - 360 - 154 = 9086 m^{2}$

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Given, dimensions of playground =120 m×80 m ∵ Area of rectangle ABCD=120×80=9600 m2 Area of rectangle GHIJ=JI×IH=2×77=154 m2 Area of rectangle ABFE=BF×AB=3×120=360 m2 ∴ Area of remaining playground = Area of rectangle ABCD - Area of rectangle ABFE - Area of GHIJ =9600−360−154=9086 m2