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]
