Question

In Figure 3. ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region. (Use π = 3.14)

Answer 1

Area of the shaded region = Area of square − (4 ⨯ Area of quarter having radius 1 cm + Area of circle having diameter 2 cm)
$$\begin{gathered} ={\left(4\right)}^2-\left[4\times \frac{1}{4}\times \mathrm{\pi }{\left(1\right)}^2+\mathrm{\pi }{\left(\frac{2}{2}\right)}^2\right] \\ =16-\left[3.14+3.14\right] \\ =16-6.28 \\ =9.72{\mathrm{cm}}^2 \end{gathered}$$
Hence, the area of shaded region is 9.72 cm²