Find the number of units in the length of diagonal $DA$ of the regular hexagon shown. Express your answer in simplest radical fo

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sergij07 [2.7K]

1 year ago

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Find the number of units in the length of diagonal $DA$ of the regular hexagon shown. Express your answer in simplest radical fo

rm.

Mathematics

1 answer:

LekaFEV [45] · Answer 1 · 2023-10-20T20:51:52+03:00

17.32 the number of units in the length of diagonal $DA$ of the regular hexagon.

<h3>How do you find the length of the diagonal of a regular hexagon?</h3>

Six equilateral triangles can be formed from the hexagon. The equilateral triangle has an equal length on each side. The diagonal of the hexagon is formed by joining two of the sum of the lengths of the equilateral triangles. As a result, the hexagon's diagonal is twice as long as its sides.

For a polygon, the SUM of the internal angles is:

(n-2) * 180 (n=6 for hexagon)

(6-2)*180 = 720 Thus EACH angle is : 720/6 = 120 degrees

Therefore, the triangle's main angle is 120 degrees, and its other two angles are equal.

There are 180 degrees in any triangle:

(180-120) / 2 = 30 degrees for each of the smaller angles.

Now use the law of sines:

10/sin30 = x/(sin120)

10/(.5) × (sqrt3 )/ 2 = x

10 sqrt 3

10/sin30 × sin 120 = 17.32

17.32 is the number of units in the length of diagonal $DA$ of the regular hexagon.