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.

Answer 1

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 $\times$ Area of a quadrant of radius 3.5m)

Now, area of the rectangular piece = 20 $\times$ 15 = 300 sq.m

And, area of a quadrant with radius 3.5 m =14$\pi r^2$ = 14$\times \frac{22}{7}\times (3.5{)}^2$

=14$\times \frac{22}{7}\times$3.5$\times$3.5 = 9.625 sq.m

∴ Area of the remaining part=300-(4$\times$9.625)=261.5 sq.m