Question

what is the area of a regular 15-gon with a perimeter of 90 m ?

Answer 1

Assuming a regular polygon, then s =90/15=6
A 15- gon has exterior angles = 360/15=24, so interior angles of 156
Form a triangle with a radius, apothem and a half- side
Then the 156/2= 78 degrees, with the apothem being opposite, and the halfside being adjacent= 3
so tan 78= a/3 and a= 3tan 78=14.114

Then area = (1/2)Pa= (1/2)(90)(a)=635.13 m^2

Answer 2

ok this makes sense, I just need a proper calculator to perform the function. but thank you, I will remember that, I have the similar example in my book, just a bit tricky.

Answer 3

Ok...I hope that helps!

Answer 4

it definitely does, thank you!