question_answer

In Fig. 4, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region, \[\left( use\,\pi =\frac{22}{7} \right)\]

Answer:

Given, a square ABCD of side 14 cm

Then, Area of square \[=\text{ (}side{{)}^{2}}\]

\[={{(14)}^{2}}=196\text{ }c{{m}^{2}}\]

2 [Area of semicircle] \[=\pi \text{ }{{r}^{2}}\]

\[=\frac{22}{7}\times \frac{14}{2}\times \frac{14}{2}=154\,c{{m}^{2}}\]

Now, Area of shaded region = 2[Area of square\[\]2 (Area of semicircle)]

\[=2\,[196-154]=2\times 42=84\text{ }c{{m}^{2}}\]