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exttt{OO} is the center of the regular hexagon below. Find its area. Round to the nearest tenth if necessary. The radius is $11$

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Circles: word problems

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Q. exttt{OO} is the center of the regular hexagon below. Find its area. Round to the nearest tenth if necessary. The radius is

11

Divide into Triangles: We know a regular hexagon can be divided into $6$ equilateral triangles. So, we'll find the area of one triangle and multiply by $6$ .
Area Formula: The formula for the area of an equilateral triangle is $A = (\sqrt{3}/4) \times \text{side}^2$ . The side of each triangle is the same as the radius, which is $11$ yards.
Calculate Side Length: Now, plug in the side length into the area formula: $A = (\sqrt{3}/4) \times 11^2$ .
Calculate Triangle Area: Calculate the area of one triangle: $A = (\sqrt{3}/4) \times 121$ .
Simplify Calculation: Simplify the calculation: $A \approx (\frac{1.732}{4}) \times 121$ .
Final Triangle Area: Do the math: $A \approx 0.433 \times 121$ .
Multiply by $6$ : Finish the calculation for one triangle's area: $A \approx 52.393$ .
Calculate Total Area: Multiply this area by $6$ to get the hexagon's area: $\text{Area}_{\text{hexagon}} \approx 6 \times 52.393$ .
Round to Nearest Tenth: Calculate the hexagon's total area: $\text{Area}_{\text{hexagon}} \approx 314.358$ .
Round to Nearest Tenth: Calculate the hexagon's total area: $\text{Area}_{\text{hexagon}} \approx 314.358$ . Round to the nearest tenth: $\text{Area}_{\text{hexagon}} \approx 314.4 \, \text{yards}^2$ .

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