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Identify the area of a regular decagon with side length 5 m rounded to the nearest tenth.
THE RED IS THE ONE I GOT WRONG

Identify The Area Of A Regular Decagon With Side Length 5 M Rounded To The Nearest Tenth THE RED IS THE ONE I GOT WRONG class=

Sagot :

ivycoveredwalls

Answer:

192.4 m^2

Step-by-step explanation:

See the attached image.

The area of a regular polygon is  [tex]A=\frac{1}{2}ap[/tex]  where p is the perimeter and  a  is the apothem (the distance from the center to the midpoint of a side).

The perimeter is  p = 10(5) = 50m.  This is a huge decagon!

Calculate the measure of angle KGL.  In a decagon, the total of all interior angles is 180(10-2) = 1440 degrees.  That makes one of the interior angles 1440 / 10 = 144, and angle KGL is half of that, 72 degrees.

To find  a, use a trigonometric ratio in right triangle GKL.  GL = 2.5, half the length of side GH.

[tex]\tan{72^\circ} = a/2.5\\\\a=2.5\tan{72^\circ} \approx 7.6942[/tex]

The area of the decagon is

[tex]A=\frac{1}{2}(7.7.6942)(50) \approx 192.4[/tex]

View image ivycoveredwalls
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