What is the approximate area of a regular hexagon with a radius of 20 units?

by

Calculating the Area of a Regular Hexagon

A regular hexagon can be defined as a six-sided polygon where all sides and angles are equal. To find the area of a regular hexagon, we can use a specific formula that relies on the radius (the distance from the center to any vertex) of the hexagon.

Formula for Area

The formula to calculate the area (
A) of a regular hexagon based on its radius (
r) is:

A = rac{3	ext{√}3}{2} r^2

Step-by-Step Calculation

For our hexagon with a radius of 20 units:

  1. First, substitute the radius into the formula:
    2. A = rac{3	ext{√}3}{2} (20)^2
  2. This simplifies to:
    3. A = rac{3	ext{√}3}{2} 	imes 400
  3. Calculating the multiplication:
    4. A = rac{1200	ext{√}3}{2}
  4. Now, divide 1200 by 2:
    5. A = 600	ext{√}3
  5. Finally, to find an approximate numerical value, we use the approximate value of √3, which is about 1.732:
    6. A ≈ 600 	imes 1.732 = 1039.2

Conclusion

Therefore, the approximate area of a regular hexagon with a radius of 20 units is about 1039.2 square units.

Leave a Comment