The area of a regular octagon is 35 cm. What is the area of a regular octagon with sides seven times as large?
+128473 The radius - r - of an octagon with side length s can be figured thusly :
(1/2)s / sin 22.5 = r = s/(2sin22.5)
And the total area is gven by
A = 8*(1/2)r^2sin45 .... and substituting for r, we have
A = 4s^2/[2sin22.5]^2 * sin 45
A = s^2 [sin45/[sin22.5]^2]
So...if the side length is 7 times as great....the area =
A = (7s)^2 [sin45/[sin22.5]^2] = 49s^2 [sin45/[sin22.5]^2] = 49 times as large = 49 x 35 = 1715 sq units
+128473 The radius - r - of an octagon with side length s can be figured thusly :
(1/2)s / sin 22.5 = r = s/(2sin22.5)
And the total area is gven by
A = 8*(1/2)r^2sin45 .... and substituting for r, we have
A = 4s^2/[2sin22.5]^2 * sin 45
A = s^2 [sin45/[sin22.5]^2]
So...if the side length is 7 times as great....the area =
A = (7s)^2 [sin45/[sin22.5]^2] = 49s^2 [sin45/[sin22.5]^2] = 49 times as large = 49 x 35 = 1715 sq units
