Question

How would you find the area of the shaded region?

Consider the following steps. Which would be the correct order to solve the above-mentioned question?
1. Find the area of each unshaded region.
2. Identify the unshaded regions.
3. Subtract the sum total of areas of unshaded regions from the area of the square.

• A. 1, 2, 3
• B. 2,1,3
• C. 3,2,1
• D. 2,3,1

Answer 1

The correct option is B 2,1,3

Consider the square and identify the two regions marked as I and II.
Find the area of each unshaded region and subtract the total area of unshaded regions from the area of the square
Area of region I = Area of square - area of the lower quarter circle.
Area of region II = Area of square - area of upper quarter circle.
So, $areaofI=areaofII=sid{e}^2-\frac{1}{4}\times \pi r^2$
$=64-\frac{1}{4}\times \frac{22}{7}\times 8^2$
$=13.72c{m}^2$

Hence Area of I + II = 13.72 +13.72 = 27.44 $c{m}^2$
So, area of the shaded region = area of square - area of I + area of II
= 64 - 27.44
$=36.56c{m}^2$