Question

A regular hexagon inscribed in a circle is approximately 0.827 times the area of that same circle. What percentage of the circle is
a. occupied by the hexagon

b. not occupied by the hexagon

Answer 1

a. The percentage of the circle occupied by the hexagon is 82.7%

b. The percentage of the circle not occupied by the hexagon is 17.3%

Step-by-step explanation:

a regular hexagon inscribed in a circle is approximately 0.827 times the

area of that same circle

1. Assume that area the circle is x

2. Find the ratio of area hexagon to area circle

3. Change The ratio to percentage

4. Subtract area hexagon from area circle to find the area not occupied

    by the hexagon and do the same steps 2 and 3 with the area not

    occupied and the circle

∵ The regular hexagon inscribed in a circle

∴ Area the circle  > area of the hexagon

∵ Area the circle is x

∵ Area the hexagon is 0.827 times the area of the circle

∴ Area hexagon = 0.827(x)

∵ The ratio between area hexagon and area circle = $\frac{0.827x}{x}$

- Cancel x up with x down

∴ The ratio between area hexagon and area circle = 0.872

- Change the ratio to percentage by multiply it by 100%

∴ The percentage of area hexagon to area circle = 0.827 × 100%

∴ The percentage of area hexagon to area circle = 82.7%

a. The percentage of the circle occupied by the hexagon is 82.7%

∵ Area the circle is x

∵ Area the hexagon is 0.827 x

∴ The area not occupied by the hexagon = x - 0.827 x

∴ The area not occupied by the hexagon = 0.173 x

The ratio between area not occupied by the hexagon and area circle

= $\frac{0.173x}{x}$

- Cancel x up with x down

∴ The ratio between area not occupied by the hexagon and area

   circle = 0.173

- Change the ratio to percentage by multiply it by 100%

∴ The percentage of area not occupied by the hexagon to area

   circle = 0.173 × 100%

∴ The percentage of area not occupied by the hexagon to area

   circle = 17.3%

b. The percentage of the circle not occupied by the hexagon is 17.3%

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