A) \[\frac{{{a}^{2}}}{2}\left( \frac{\pi }{2}-1 \right)\text{sq}\,\,\text{units}\]
B) \[{{a}^{2}}(\pi -1)\text{sq}\,\,\text{units}\]
C) \[{{a}^{2}}\left( \frac{\pi }{2}-1 \right)\text{sq}\,\,\text{units}\]
D) \[\frac{{{a}^{2}}}{2}(\pi -1)\text{sq}\,\,\text{units}\]
Correct Answer: C
Solution :
Radius of circle = a units |
\[\therefore \]Area of semi-circle \[=\frac{\pi {{a}^{2}}}{2}\text{sq}\,\,\text{units}\] |
Both \[\Delta ABC\]and \[\Delta BCD\]are isosceles and equal. |
\[\therefore \]Area of each triangle \[=\frac{1}{2}{{a}^{2}}\] |
\[\therefore \]Area of both triangles \[=2\times \frac{1}{2}{{a}^{2}}={{a}^{2}}\,\,\text{sq}\,\,\text{units}\] |
Area of shaded region |
\[=\frac{\pi {{a}^{2}}}{2}-{{a}^{2}}={{a}^{2}}\left( \frac{\pi }{2}-1 \right)\,\,\text{sq}\,\,\text{units}\] |
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