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 ⇒lb−πb24 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×b−π(b2)2 ⇒lb−πb24 We can see that the areas of the shaded regions are same in both the figures.

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