Find the area of the regular polygon

Question

6.16 yd
4yd

Answer 1

To find the area of a regular polygon, you can use the formula:

Area = (perimeter * apothem) / 2

First, calculate the perimeter of the regular polygon:

Perimeter = number of sides * length of each side
Perimeter = 6 * 4 yd
Perimeter = 24 yd

Next, calculate the apothem of the regular polygon. The apothem is the perpendicular distance from the center of the polygon to a side.

Apothem = side length / (2 * tan(180 degrees / number of sides))
Apothem = 4 yd / (2 * tan(180 degrees / 6))
Apothem = 4 yd / (2 * tan(30 degrees))
Apothem = 4 yd / (2 * 0.5774)
Apothem = 3.464 yd

Now, plug the values into the area formula:

Area = (24 yd * 3.464 yd) / 2
Area = 83.136 yd^2

Therefore, the area of the regular polygon is 83.136 square yards.