A regular hexagon is inscribed in a circle of radius $10$ cm. The area of the hexagon is :
$150 \sqrt{3}$ sq. cm.
$25 \sqrt{3}$ sq. cm.
$150$ sq. cm.
$600$ sq. cm.
$300 \sqrt{3}$ sq. cm.

Question

A regular hexagon is inscribed in a circle of radius 10 cm- The area of the hexagon is -150 sqrt-3-sq- cm-25 sqrt-3- sq- cm-150 sq- cm-600 sq- cm-300 sqrt-3- sq- cm-

Toppr Admin · Accepted Answer

Given radius -10cm -x21D2-side -10cm as triangle formed here is an equilateral trinagle-x2234-area-6-xD7-x221A-34a2-x21D2-area-3-x221A-32-xD7-102-x2234-area-150-x221A-3

A regular hexagon is inscribed in a circle of radius 10 cm. The area of the hexagon is :150√3sq. cm.25√3 sq. cm.150 sq. cm.600 sq. cm.300√3 sq. cm.

Given radius =10cm ⇒side =10cm as triangle formed here is an equilateral trinagle.∴area=6×√34a2⇒area=3√32×102∴area=150√3

A regular hexagon is inscribed in a circle of radius $10$ cm. The area of the hexagon is :
$150 \sqrt{3}$ sq. cm.
$25 \sqrt{3}$ sq. cm.
$150$ sq. cm.
$600$ sq. cm.
$300 \sqrt{3}$ sq. cm.

Given radius $= 10 c m$ $\Rightarrow$ side $= 10 c m$ as triangle formed here is an equilateral trinagle.

$∴ a r e a = 6 \times \frac{\sqrt{3}}{4} a^{2}$

$\Rightarrow a r e a = \frac{3 \sqrt{3}}{2} \times 10^{2}$

$∴ a r e a = 150 \sqrt{3}$