find the area of a regular hexagon with radius 12 in round to the nearest whole number

find the area of a regular hexagon with radius 12 in round to the nearest whole number

The Correct Answer and Explanation is:

To find the area of a regular hexagon circumscribed about a circle, you need to know the relationship between the radius of the circle and the side length of the hexagon.

Step 1: Relationship Between the Radius and the Side Length

In a regular hexagon, each side length is equal to the radius of the circumscribed circle. Therefore, if the radius of the circle is 12 units, the side length of the hexagon is also 12 units.

Step 2: Formula for the Area of a Regular Hexagon

The formula to calculate the area of a regular hexagon is: A=332×s2A = \frac{3\sqrt{3}}{2} \times s^2A=233​​×s2

Where:

• AAA is the area of the hexagon,
• sss is the side length of the hexagon.

Step 3: Substituting the Side Length

Since the side length s=12s = 12s=12 units, we can substitute this value into the formula: A=332×122A = \frac{3\sqrt{3}}{2} \times 12^2A=233​​×122 A=332×144A = \frac{3\sqrt{3}}{2} \times 144A=233​​×144 A=43232A = \frac{432\sqrt{3}}{2}A=24323​​ A=2163A = 216\sqrt{3}A=2163​

Step 4: Approximate Value of 3\sqrt{3}3​

The approximate value of 3\sqrt{3}3​ is 1.732. So: A=216×1.732A = 216 \times 1.732A=216×1.732 A≈374.592A \approx 374.592A≈374.592

Step 5: Rounding to the Nearest Whole Number

Rounding the result to the nearest whole number: A≈375 square unitsA \approx 375 \, \text{square units}A≈375square units

Final Answer

The area of the regular hexagon is approximately 375 square units.