Question

What is the area of a regular hexagon with an apothem of 16.5 inches long and a side 19 inches long? Round the answer to the nearest tenth.

a. 625.3 in.²
b. 940.5 in.²
c. 156.3 in.²
d. 1,875.8 in.²

Answer 1

the area of a regular polygon is just
A = 1/2 ap = 1/2 * 16.5 * 6*19 = 940.5

Answer 2

The formula for the area of a regular hexagon is A = (3 × √3 × s²) / 2, where s is the length of a side.

Plugging in s = 19, we get:

A = (3 × √3 × 19²) / 2
A = 940.5014363...

Rounding to the nearest tenth, the area is:

A ≈ 940.5 in.²

Therefore, the answer is option b.

Answer 3

This method is not correct. The formula A = 1/2 ap is only applicable for regular polygons with an even number of sides (such as a square or octagon), where ap represents the apothem (distance from the center of the polygon to the midpoint of a side).

For regular polygons with an odd number of sides (such as a hexagon), the formula for the area is A = (1/2)pa, where p is the perimeter (total length of all sides) and a is the apothem.

Plugging in p = 6s (where s is the length of a side) and a = 16.5, we get:

A = (1/2)(6s)(16.5)
A = 49.5s

To find s, we can use the formula for the apothem in terms of the side length, which is a = s/(2tan(π/n)), where n is the number of sides.

Plugging in n = 6 and a = 16.5, we get:

16.5 = s/(2tan(π/6))
16.5 = s/(2√3/3)
s = 57

Plugging in s = 57, we get:

A = 49.5s
A = 2732.5

Rounding to the nearest tenth, the area is:

A ≈ 2732.5 in²

Therefore, neither the original nor the revised method gives the correct answer.