Question

find the area of the shaded portion:
16 cm
16 cm
16 cm
16 cm
55.04 sq.cm
62.44 sq.cm
65.64 sq.cm
42.84 sq.cm

Explanation:

Step1: Find area of square

The square has side length \( 16 \, \text{cm} \). The area of a square is \( \text{side}^2 \), so:
\( \text{Area of square} = 16^2 = 256 \, \text{sq.cm} \)

Step2: Find area of 4 quarter - circles (equivalent to 1 circle)

The radius \( r \) of each quarter - circle is half of the side of the square, so \( r=\frac{16}{2}=8 \, \text{cm} \).
The area of a circle is \( \pi r^2 \), taking \( \pi = 3.14 \):
\( \text{Area of circle} = 3.14\times8^2=3.14\times64 = 200.96 \, \text{sq.cm} \)

Step3: Find area of shaded region

The area of the shaded region is the area of the square minus the area of the circle (since the un - shaded region is 4 quarter - circles which make a full circle):
\( \text{Area of shaded region}=256 - 200.96=55.04 \, \text{sq.cm} \)

Answer:

55.04 sq.cm