The areas of the shaded regions in figures 1 and 2 are equal. The corresponding lengths and breadths of both the rectangles are equal, and the radius of the quarter circles in figure 1 is half the breadth of the rectangle.

True

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False

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Solution

The correct option is A
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 = $\frac{B r e a d t h o f R e c t a n g l e}{2}$
Therefore, $A r e a o f t h e r e g i o n s h a d e d i n r e d = A r e a o f t h e r e c t a n g l e - A r e a o f t h e c i r c l e o f r a d i u s (= \frac{B r e a d t h o f R e c t a n g l e}{2})$ .

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.
Therefore, $A r e a o f t h e r e g i o n s h a d e d i n r e d = A r e a o f t h e r e c t a n g l e - A r e a o f t h e c i r c l e o f r a d i u s (= \frac{B r e a d t h o f R e c t a n g l e}{2})$ .
We can see that the areas of the shaded regions are same in both the figures.

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Similar questions

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.]

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.