Question

a rectangular piece of paper is 25cm long and 16 cm wide.from its four corners, quadrants of radii 7 cm have been cut. find the area of remaining part.

Answer 1

Area of rectangle - area of 4 quadrant
25*16-4*1/4*22/7*7*7
400-154
=246

Answer 2

Consider, the area of the rectangular piece of paper;
area of rectangle = ( length × breadth )
= 25 × 16
= 400 cm² ----( i )
Now, if a quadrant of radius 7 cm is cut from the all four corners then then area occupied by the the four quadrants will be equal to area of a circle ( four quadrants = one complete circle)
Now, area occupied by the four quadrants is equal to the area of circle
Therefore, area of quadrants = pi × r²
= (22÷7) × ( 7 )²
= 22 ÷ 7 × 49
= 22 × 7
= 154 cm²----( ii )
Therefore, the area of the remaining part
= area of. - area of quadrants
rectangle
= 400 - 154 ------ from equation ( i )
and ( ii )
= 246 cm²
Therefore, the area of the remaining part is 246 cm²