A) \[\frac{\pi }{2}({{a}^{2}}+{{b}^{2}})+\frac{1}{8}{{(a+b)}^{2}}\]
B) \[\frac{\pi }{2}({{a}^{2}}+{{b}^{2}})+\frac{1}{2}ab\]
C) \[\frac{\pi }{2}({{a}^{2}}+{{b}^{2}})+\frac{1}{8}{{(a+b)}^{2}}\]
D) \[\frac{\pi }{4}({{a}^{2}}+{{b}^{2}})+\frac{1}{2}ab\]
Correct Answer: D
Solution :
Total area \[=I+II+III+IV\] \[=\frac{1}{2}\pi {{\left( \frac{a}{2} \right)}^{2}}+\frac{1}{2}\pi {{\left( \frac{b}{2} \right)}^{2}}+\frac{1}{2}\pi {{\left( \frac{\sqrt{{{a}^{2}}+{{b}^{2}}}}{2} \right)}^{2}}+\frac{1}{2}ab\] \[=\frac{\pi }{8}({{a}^{2}}+{{b}^{2}})+\frac{\pi }{8}({{a}^{2}}+{{b}^{2}})+\frac{1}{2}ab\] \[=\frac{\pi }{4}({{a}^{2}}+{{b}^{2}})+\frac{1}{2}ab\]You need to login to perform this action.
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