How do you calculate the area of a regular hexagon with a radius of 6 inches?

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Calculating the Area of a Regular Hexagon

To find the area of a regular hexagon, we can use the formula:

A = rac{3	ext{√3}}{2} 	imes r^2

Where A is the area and r is the radius of the circumscribed circle (which is also the distance from the center to a vertex). In this case, the radius r is 6 inches.

Step-by-Step Calculation:

  1. Plug the radius into the formula:
    2. A = rac{3	ext{√3}}{2} 	imes (6)^2
  2. Calculate the square of the radius:
    3. A = rac{3	ext{√3}}{2} 	imes 36
  3. Now, simplify the expression:
    4. A = rac{108	ext{√3}}{2}
  4. Finally, compute the division:
    5. A = 54	ext{√3}

To get a numerical estimate of the area, we can approximate √3 as about 1.732:

A ≈ 54 	imes 1.732 ≈ 93.536 	ext{ square inches}

Final Result

Thus, the area of the regular hexagon with a radius of 6 inches is approximately 93.54 square inches.

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