Question

A regular hexagon is shown.


A regular hexagon with a radius of 10 inches 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

Answer:

(C)9 in.

Step-by-step explanation:

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

Given the hexagon with a radius of 10 inches

The apothem AB divides the side of the hexagon into two equal parts of 5 Inches as seen in the attached diagram.

Using Pythagoras Theorem

$10^2=5^2+|AB|^2\\|AB|^2=10^2-5^2\\|AB|^2=75\\|AB|=\sqrt{75}\\ |AB|=8.66 in\\\approx 9 in (rounded to the nearest inch)$

The correct option is C

Answer 2

The length of the apothem is : 9 inches

What is a hexagon?

A hexagon is a polygon with six sides and six angles.

Analysis:

Since the radius of the polygon is the distance from the center of the face of the polygon to its vertex, then the apothem which is the distance from the center to the mid point of the side forms right angle triangle with the radius and half the base.

So,

$radius^{2}$ = $apothem^{2}$ + $side/2^{2}$

$10^{2}$ =  $apothem^{2}$ + $10/2^{2}$

100 =  $apothem^{2}$ + 25

$apothem^{2}$ = 100 - 25

apothem = $\sqrt{75}$ = 8.66 = 9 inches

In conclusion, the length of the apothem  is 9 inches

Learn more about hexagon: brainly.com/question/118422

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