A) \[\frac{{{a}^{2}}}{2}+\frac{\sqrt{3}}{8}{{a}^{2}}\]
B) \[\frac{{{a}^{3}}}{2}+\frac{\sqrt{3}}{4}{{a}^{3}}\]
C) \[{{a}^{3}}+\sqrt{3}{{a}^{3}}\]
D) \[\frac{{{a}^{3}}}{2}+\frac{\sqrt{3}}{2}{{a}^{3}}\]
Correct Answer: A
Solution :
As, OAB is equilateral triangle. |
\[\therefore \] \[\angle OAM=60{}^\circ \]and AB = OA = OB = a |
\[\therefore \] (Altitude) \[OM=\frac{\sqrt{3}}{2}\]side \[=\frac{\sqrt{3}}{2}a\] |
\[\therefore \] \[OL=OM+ML=\frac{\sqrt{3}}{2}a+a\] |
\[\therefore \] Area of trapezium \[\frac{1}{2}(AD+OL)AM\] |
\[=\frac{1}{2}\left( a+\frac{\sqrt{3}}{2}a+a \right)\frac{a}{2}\left( \because AM=\frac{1}{2}AB \right)\] |
\[=\frac{\sqrt{3}}{2}{{a}^{2}}+\frac{{{a}^{2}}}{2}\] |
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