Semicircles are drawn outside by taking every side of regular hexagon as a diameter. The ;perimeter of hexagon is 60 cm. Find the area of complete figure formed as such.($\pi$ = 3.14) ($\sqrt3$ = 1.73)

Formula: The area of a hexagon=$\quad \dfrac { 3\sqrt { 3 } }{ 2 } { side }^{ 2 }.\quad$

There are 6 semicircles=3 circles.

radius of each circle=r=$\quad \dfrac { 1 }{ 2 } \times$side of the hexagon.

ar.complete figure=ar.hexagon+3(ar.circle).

Here ,

perimeter of the regular hexagon=60cm.

So one side=$\quad \dfrac { 60 }{ 6 } cm=10cm.\\ \therefore \quad ar.hexagon\\ =\dfrac { 3\sqrt { 3 } }{ 2 } { side }^{ 2 }\\ =\dfrac { 3\sqrt { 3 } }{ 2 } { 10 }^{ 2 }{ cm }^{ 2 }\\ =\dfrac { 3\times 1.73\times 100 }{ 2 } { cm }^{ 2 }\\ =259.5{ cm }^{ 2 }.\quad$

Again radius of each circle=r=$\quad \dfrac { 1 }{ 2 } \times$side of the hexagon= $\dfrac{10}{2}cm=5cm.$

$\quad ar.(3circles)=3\times \pi \times { r }^{ 2 }\\ =3\times 3.14\times 5\times 5{ cm }^{ 2 }\\ =235.5{ cm }^{ 2 }.\quad$

So ar.complete figure=ar.hexagon+3(ar.circle).

$=(259.5+235.5)$ $\quad { cm }^{ 2 }\quad$

=495$\quad { cm }^{ 2 }$