Question

O is the center of the regular hexagon below. Find its area. Round to the nearest tenth if necessary.

Answer 1

The area of the regular hexagon is 166.3 square units (to the nearest tenth).

Explanation:

The formula for the area of a regular polygon is:

`\boxed{\textsf{Area}=(r^2n\sin\left((360^(\circ))/(n)\right))/(2)}`

where:

• r is the radius (the distance from the center to a vertex).
• n is the number of sides.

From inspection of the given regular polygon:

• r = 8 units
• n = 6

Substitute the values into the formula and solve for area:

`\begin{aligned}\textsf{Area}&=(8^2\cdot 6 \cdot \sin\left((360^(\circ))/(6)\right))/(2)\\\\&=(64\cdot 6 \cdot \sin\left(60^(\circ)\right))/(2)\\\\&=(384 \cdot (√(3))/(2))/(2)\\\\&=(192√(3))/(2)\\\\&=96√(3)\\\\&=166.3\; \sf square\;units\;(nearest\;tenth)\end{aligned}`

Therefore, the area of the regular hexagon is 166.3 square units (to the nearest tenth).