A regular hexagon is inscribed in …
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Sia ? 6 years, 6 months ago
Consider the following figure:
We know that the regular hexagon is a combination of 6 equilateral triangles.
{tex}\therefore{/tex} Area of a hexagon = 6 {tex}\times{/tex} Area of {tex}\Delta O A B{/tex}
{tex}\Rightarrow \text { Area of } \Delta O A B = \frac { 24 \sqrt { 3 } } { 6 } = 4 \sqrt { 3 } \mathrm { cm } ^ { 2 }{/tex}
{tex}\Rightarrow \frac { \sqrt { 3 } } { 4 } ( \text { side } ) ^ { 2 } = 4 \sqrt { 3 }{/tex}
{tex}\Rightarrow ( \text { side } ) ^ { 2 } = 4 \sqrt { 3 } \times \frac { 4 } { \sqrt { 3 } } = 16{/tex}
{tex}\Rightarrow{/tex} side = 4 cm
{tex}\Rightarrow{/tex} Radius of a circle = 4 cm
{tex}\therefore{/tex} Area of a circle {tex}= \pi r ^ { 2 } = 3.14 \times 4 \times 4 = 50.24 \mathrm { cm } ^ { 2 }{/tex}
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