MATH SOLVE

5 months ago

Q:
# 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.

Accepted Solution

A:

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:

[tex]x \: \\ x \sqrt{3} \\ and \: 2x[/tex]

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:

[tex]x \sqrt{3} = 5 \sqrt{3} = 8.66[/tex]

So rounded up, you apothem then is closest to D) 9 in.

In a 30-60-90 triangle, the sides are is the ratio of:

[tex]x \: \\ x \sqrt{3} \\ and \: 2x[/tex]

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:

[tex]x \sqrt{3} = 5 \sqrt{3} = 8.66[/tex]

So rounded up, you apothem then is closest to D) 9 in.