Download Kyle is installing an octagon shaped window in - ontrack

Kyle is installing an octagon shaped window in his house. He is told that the Perimeter
of the entire window is 96 inches. What will be the area of this window?
Given that the Perimeter is 96 inches, we
know that the length of each side will be 12
inches because = 12
Now that we know the length of each side,
construct the apothem and one triangle.
Around the center point of the polygon the
sum of the central angles found in the top of
each triangle would be 360 degrees. Dividing
360 by 8 we find that each triangle would have
a 45 degree angle. However, the apothem
bisects that angle as well as the side of the
octagon, giving the right triangle an angle of
22.5 degrees and a base of 6 inches.
Using the Right Triangle Trigonometry, we
must take the Tangent of 22.5 degrees to find
the measurement of the apothem.
6
tan(22.5) = 6
tan(22.5)
= 14.485
Since the apothem measures approximately
15.679 inches and we know the total
perimeter, we can apply our formula of =
, where a is the length of the apothem and
P is the total Perimeter.
=
Thus,
=
1
= (14.485)(96)
2
1
= (1390.56)
2
= 695.28