Question

How would you go about finding the area of the shaded region?

• A. (Area of I + Area of II) + (Area of III + Area of IV)
• B. (Area of I + Area of III) + (Area of II + Area of IV)
• C. (Area of I + Area of IV) + (Area of II + Area of III)
• D. (Area of I + Area of II) $\times$ 2

Answer 1

The correct option is B (Area of I + Area of III) + (Area of II + Area of IV)


We would find the area of unshaded region that are opposite to each other and by taking them in pairs.
Area of shaded regions, I +III = II+IV = Area of square - Area of 2 semicircles(which includes I and III as the shaded portions)
$=sid{e}^2-\frac{2\times \pi r^2}{2}$
$=sid{e}^2-\pi r^2$