Question

a quarter circle is drawn in each corner of the square. find area of shaded portion.

Answer 1

here is your answer ...hope u will understand

Answer 2

The area of shaded portion is 168 $(cm^{2})$.

Step-by-step explanation:

1. Size of sides of square (a) = 28 (cm)

2. Radius of quadrant circle ( R) $=\frac{a}{2}=\frac{28}{2}=14 (cm)$

3. Area of Square$(A_{sq})$

   $A_{sq}=(side)^{2}=(a)^{2}=28^{2}=784 (cm^{2})$     ...1)

4.Area of quadrant circle$(A_{qc})$

  $A_{qc}=\frac{\pi \times R^{2}}{4}$       ...2)

  Taking $\pi =\frac{22}{7}$

  $A_{qc}=\frac{\pi \times R^{2}}{4}=\frac{22\times 14^{2}}{7\times 4}$   ...3)

5. So

   Area of shaded region = Area of square - 4×Area of one quadrant circle

   Then

   Area of shaded region $=A_{sq}-4\times A_{qc}$

   From equation 1) and equation 3)

   Area of shaded region $=784-4\times (\frac{22\times 14^{2}}{7\times 4})=168 (cm^{2})$