#### Question

A rectangular piece is 20 m long and 15 m wide. From its four corners, quadrants of radii 3.5 m have been cut. Find the area of the remaining part.

#### Solution

It is given that the length of the rectangular piece is 20 m and its width is 15 m .

And, from each corner a quadrant each of radius 3 . 5 m has been cut out .

A rough figure for this is given below:

∴ Area of the remaining part = Area of the rectangular piece - (4 x Area of a quadrant of radius 3 . 5m)

Now, area of the rectangular piece = \[20 \times 15 = 300 m^2 \]

And, area of a quadrant with radius \[3 . 5 m =\frac{1}{4} \pi r^2 = \frac{1}{4} \times \frac{22}{7} \times (3 . 5 )^2 \]

\[ = \frac{1}{4} \times \frac{22}{7} \times 3 . 5 \times 3 . 5\]

\[ = 9 . 625 m^2 \]

∴ Area of the remaining part = \[ 300 - (4 \times 9 . 625) = 261 . 5 m^2\]