A square tile of length 20 cm has four quarter circles at each corner as shown in figure below. Determine the area of the shaded portion.

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cm 2

cm 2

cm 2

106

cm 2

answer is B.

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Detailed Solution

Given, a square tile of length 20 cm has four quarter circles at each corner.
The area of any square of side length ‘a’ is the square of its side, i.e.,

a 2

.
Next, the area of a circle with ‘r’ radius is given as

π r 2

.
Now, we can observe in the given figure that four quarter circles are present inside the square.
So, the area of all these quarter circles taken together will be equal to the area of a complete circle.
Then, the area of the shaded portion = Total area of the square – Area of the complete circle
=

a 2

π r 2

Now, as per the question, the value of a = 20 and the radius of the complete circle is half of the side length i.e., 10 cm as can be observed in the diagram.
So we get the area of the shaded portion as follows,