Two semicircles are drawn in a square with sides as diameters as shown. If the side of the square is 2 units, how much is the shaded area (in sq. units)?

Correct option is C

Given:
Square side = 2 units
Two semicircles are drawn using the adjacent sides of the square as diameters
Find the shaded area

Solution:

Now, divide the large square into 4 equal smaller squares (as shown in Fig. I)

• Each small square has area = 1 sq. unit

To find the shaded region, remove the unshaded parts (Fig. II)

• Area of the new shape = 3 sq. units (after removing one small square without shading)

• The area to subtract = area of 2 quadrants (a and b)
  Each quadrant has radius = 1 unit
  So, area of one quadrant = $$\text = \frac{1}{4} \pi r^2 = \frac{1}{4} \pi (1)^2 = \frac{\pi}{4} \\$$​​

  14πr2=14π(1)2=π4\frac{1}{4} \pi r^2 = \frac{1}{4} \pi (1)^2 = \frac{\pi}{4}

​$$\text{Total area of 2 quadrants} = 2 \times \frac{\pi}{4} = \frac{\pi}{2} \\\text{Shaded Area} = 3 - \frac{\pi}{2}$$

Final Answer: 3 - π/2​​