Question

A rectangular path of $\sqrt{2}m$ width is made in a square lawn as shown in the figure.
What is the remaining area of the lawn? (Given: $EH\parallel BD$)

• A. $82m^2$
• B. $82\sqrt{2}{m}^2$
• C. $92\sqrt{2}{m}^2$
• D. $92m^2$

Answer 1

The correct option is A

$82m^2$

Area of lawn $={10}^2=100m^2$

Since all the points E, F, G and H lie on the boundary of the square, BE = BF.

BE = BF = 1 m (Using Pythagoras Theorem)

So, FC = GC = 9 m

$FG=9\sqrt{2}m$ (Using Pythagoras Theorem)

Area of rectangular path $=9\sqrt{2}\times \sqrt{2}=18m^2$

Area of remaining lawn $=(100-18)m^2=82m^2$