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Question

State true or False.
Areas of the shaded regions in figures 1 and 2 are equal. The corresponding lengths and breadths of the rectangles are equal, and the radius of the quarter circles in figure 1 is half the breadth of the rectangle.


A
True
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B
False
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Solution

The correct option is B True


Area of the region shaded in red in figure 1 = Area of the rectangle - Area of the four quarter circles.
Radius of each quarter circle = Breadth of Rectangle2 = b2

Area of rectangle =l×b=lb
Area of 4 quarter circles =4×πr24
=πb24

Therefore, Area of region in red = Area of rectangle - Area of 4 quarter circles
lbπb24


Therefore, Area of the region shaded in red in figure 2 = Area of the rectangle - Area of the circle inside the rectangle.
Here, observe that diameter of the circle = Breadth of the rectangle
Radius of circle = b2

Therefore, area of region in red = Area of rectangle - Area of circle
l×bπ(b2)2
lbπb24


We can see that the areas of the shaded regions are same in both the figures.


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