The area of the shaded region in the figure given below is |
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 :
Area of semi-circle \[=\frac{\pi {{a}^{2}}}{2}\] |
Now, area of \[\Delta ABD=\frac{1}{2}\times 2a\times a\] |
\[={{a}^{2}}\] |
\[\therefore \]Area of shaded region |
\[=\frac{\pi {{a}^{2}}}{2}-{{a}^{2}}\] |
\[={{a}^{2}}\left( \frac{\pi }{2}-1 \right)\,\,\text{sq}\,\,\text{units}\] |
You need to login to perform this action.
You will be redirected in
3 sec