Question

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) ($\sqrt{3}$ = 1.73)

• A. 495 c$m^2$
• B. 259.5c$m^2$
• C. 235.5c$m^2$
• D. 695.5c$m^2$

Answer 1

The correct option is A 495 c$m^2$

The area of a hexagon=$\frac{3\sqrt{3}}{2}{side}^2.$

There are 6 semicircles=3 circles.

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

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

Here ,

perimeter of the regular hexagon=60cm.

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

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

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

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

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

=495${cm}^2$

Ans- Option A