Question

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
• B. False

Answer 1

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 = $\frac{\text{Breadth of Rectangle}}{2}$
Therefore, Area of the region shaded in red = Area of the rectangle - Area of the circle of radius $(=\frac{\text{Breadth of Rectangle}}{2})$.

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, Area of the region shaded in red = Area of the rectangle - Area of the circle of radius $(=\frac{\text{Breadth of Rectangle}}{2})$.
We can see that the areas of the shaded regions are same in both the figures.