Area of polygon quick check math 6B 6.23

Answer 1

To find the area of a polygon, you can use the formula A = 1/2 * ap where a is the apothem (the perpendicular distance from the center of the polygon to a side) and p is the perimeter of the polygon.

Let's say you have a regular hexagon with a side length of 4 units. You can find the apothem of the hexagon by drawing a line from the center of the hexagon to the midpoint of one of its sides, creating a right triangle. The apothem would be the height of this triangle.

Using the Pythagorean theorem, we can find the apothem:
a^2 + (4/2)^2 = 4^2
a^2 + 2^2 = 16
a^2 + 4 = 16
a^2 = 12
a = √12
a ≈ 3.46

The perimeter of the hexagon would be 6 * 4 = 24 units.

Now, plug the values into the formula:
A = 1/2 * 3.46 * 24
A ≈ 41.52 square units

Therefore, the area of the regular hexagon is approximately 41.52 square units.