Question

A regular hexagon is shown.



What is the length of the apothem, rounded to the nearest inch? Recall that in a regular hexagon, the length of the radius is equal to the length of each side of the hexagon.
4 in.
5 in.
9 in.
11 in.

Answer 1

Since the triangle will be a 30-60-90, because 360°/6 = 60° for each central angle, then that is bisected to find the height of each of the 6 equilateral triangles. This height is the same as the apothem.
In a 30-60-90 triangle, the sides are is the ratio of:
$x \: \\ x \sqrt{3} \\ and \: 2x$
where x is opposite the 30° and 2x is opposite the 90°
Since the base is 10 and the hypotenuse is 10, 1/2 that is 5 (the x), and so:
$x \sqrt{3} = 5 \sqrt{3} = 8.66$
So rounded up, you apothem then is closest to D) 9 in.

Answer 2

The length of the apothem of a regular polygon that has a radius of 10 inches would be 9 inches .

What is the apothem of a regular polygon?

The apothem of a regular polygon is defined as a line segment from the center to the midpoint of one of its sides.

It is Given that the hexagon has a radius of 10 inches and the length of the radius is equal to the length of each side of the hexagon.

The apothem AB divides the side of the hexagon into two equal parts of 5 Inches.

Using Pythagoras Theorem

$10^2 = 5^2 + AB^2\\AB^2 = 10^2 -5^2\\AB^2 = 100 - 25\\AB^2 = 75\\AB = \sqrt{75}$

AB = 8.66

So, rounded up, we get the apothem closest to D that is 9 in.

Learn more about the apothem;

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