question_answer

ABCD is a square of side a cm. AB, BC, CD and AD all are the chords of circles with equal radii each. If the chords subtends an angle of \[120{}^\circ \] at their respective centres, find the total area of the given figure where arcs are part of the circles:

A)  \[\left[ {{a}^{2}}+4\left( \frac{\pi {{a}^{2}}}{9}-\frac{{{a}^{2}}}{3\sqrt{2}} \right) \right]\]

B)  \[\left[ {{a}^{2}}+4\left( \frac{\pi {{a}^{2}}}{9}-\frac{{{a}^{2}}}{4\sqrt{3}} \right) \right]\]

C)  \[\left[ 9{{a}^{2}}-4\pi +3\sqrt{3}\,{{a}^{2}} \right]\]

D)  \[\left[ 9{{a}^{2}}+4\pi -3\sqrt{3}\,{{a}^{2}} \right]\]

E)  None of these