Question

A rectangular piece is 20 meter long and 15 meter wide. From its four corners, quadrants of radii 3.5 meter 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 :

Therefore, Area of the remaining part = Area of the rectangular piece — (4 × Area of a quadrant of radius 3.5m)

Now, area of the rectangular piece = 20 × 15 = 300 m2

And, area of a quadrant with radius 3.5 m = 14πr2 = 14 × 227 × 3.52 = 9.625 m2

Therefore, Area of the remaining part = 300 – (4 ×9.625) = 261.5 m2