A hexagon is inscribed in a circle of radius r. Show that the ratio of the area of the hexagon to the area of the circle is equal to 3sqrt(3)2π 0.827. Can you see why the answer is exactly twice the answer to Question 28? [Page No. 148]

For regular hexagon inscribed in circle of radius r: Side of hexagon = r Area of regular hexagon = 3sqrt(3)2 × r2 Area of circle = π r2 Ratio = 3sqrt(3)r22π r2 = 3sqrt(3)2π 0.827. Hence, proved.

Question:

A hexagon is inscribed in a circle of radius $r$ . Show that the ratio of the area of the hexagon to the area of the circle is equal to $\frac{3\sqrt{3}}{2\pi} \approx 0.827$ . Can you see why the answer is exactly twice the answer to Question 28? [Page No. 148]

Answer: Verified

For regular hexagon inscribed in circle of radius $r$ :

Side of hexagon = $r$

$\text{Area of regular hexagon} = \frac{3\sqrt{3}}{2} \times r^2$

$\text{Area of circle} = \pi r^2$

$\text{Ratio} = \frac{\frac{3\sqrt{3}r^{2}}{2}}{\pi r^{2}} = \frac{3\sqrt{3}}{2\pi} \approx 0.827.$

Hence, proved.

A hexagon is inscribed in a circle of radius rrr. Show that the ratio of the area of the hexagon to the area of the circle is equal to 332π≈0.827\frac{3\sqrt{3}}{2\pi} \approx 0.8272π33​​≈0.827. Can you see why the answer is exactly twice the answer to Question 28? [Page No. 148]

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A hexagon is inscribed in a circle of radius $r$ . Show that the ratio of the area of the hexagon to the area of the circle is equal to $\frac{3\sqrt{3}}{2\pi} \approx 0.827$ . Can you see why the answer is exactly twice the answer to Question 28? [Page No. 148]