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A square lawn has a 2 m wide path surrounding it. If the area of the path is 136 m2, find the area of lawn.

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Let the side of the lawn = am 

Then side of big square = (a + 2(2)) m

= (a + 4)m

Area of the path – Area of large square – Area of smaller square 

136 = (a + 4)2 – a2 

136 = a2 + (2 x a x 4) + 42 – a2 

136 = a2 + 8a + 16 – a2 

136 = 8a + 16 

136 = 8(a + 2) 

Dividing by 8 

17 = a + 2 

Subtracting 2 on both sides 

17 – 3 = a + 2 – 2 

15 = a 

∴ Side of small square = 15 m 

Area of square = (side x side) sq. units 

∴ Area of the lawn = (15 x 15)m = 225 m 

∴ Area of the lawn = 225 m2

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