what is the apothem of a regular hexagon with sides of 16 inches?
the answer to your question would be
X = 8 tan 60 = 8 sqrt 3
To determine the apothem of a regular hexagon, you can use the formula:
Apothem = (Side length) / 2 * tan(180° / Number of sides)
In this case, the side length is given as 16 inches, and the number of sides for a hexagon is 6.
Using the formula, we can calculate the apothem as follows:
Apothem = (16) / (2 * tan(180° / 6))
First, let's simplify the formula:
Apothem = 16 / (2 * tan(30°))
Now, let's calculate the tangent of 30°, which is √3 / 3:
Apothem = 16 / (2 * (√3 / 3))
Next, multiply the denominator by 2:
Apothem = 16 / (2 * √3 / 3)
To divide by a fraction, we can multiply by its reciprocal:
Apothem = 16 * (3 / (2 * √3))
Simplifying further:
Apothem = (16 * 3) / (2 * √3)
Apothem = 48 / (2 * √3)
Finally, we can simplify by multiplying numerator and denominator by √3:
Apothem = (48 * √3) / (2 * √3 * √3)
Apothem = (48 * √3) / (2 * 3)
Apothem = 8√3
Therefore, the apothem of a regular hexagon with sides of 16 inches is 8√3 inches.
To find the apothem of a regular hexagon, you need to know the length of the side of the hexagon. The apothem is a line segment drawn from the center of the hexagon to the midpoint of any one of its sides, forming a right angle with that side.
In this case, you mentioned that the side length of the regular hexagon is 16 inches. To find the apothem, we can use the formula:
Apothem = (Side Length) / (2 * tan(π / 6))
First, determine the value of the tangent of π / 6. In radians, π / 6 is equivalent to 30 degrees. The tangent of 30 degrees is approximately 0.5774.
Next, substitute the given values into the formula:
Apothem = (16) / (2 * 0.5774)
Apothem ≈ 27.7124 inches
Thus, the apothem of the regular hexagon with sides of 16 inches is approximately 27.7124 inches.
It is the distance from the center to the midpoint of a side.
That is the leg of a right triangle whose other leg is 8 inches.
Each of the interior angles of the hexgagon is [180 - (360/6)] = 120 so the angle in our right triangle is 120/2 = 60 degrees
tan 60 =x/8
x = 8 tan 60 = 8 sqrt 3