An octagon has area 80 cm2 and shortest side with length 5 cm. A similar octagon has shortest side of length 4 cm. What is the area of this similar octagon? Include all work and any formulas used in your answer.
ps its not a test for those of you who think i need to do my own work..it a just for fun paper
2007-08-16 12:58:36 · 3 answers · asked by Alexa N 1 in Science & Mathematics ➔ Mathematics
For similar shapes, the area goes as the square of the ratio of dimensions. The similar octagon is 4/5 as large, so its area is (4/5)^2 as large:
80 * (4/5)^2 =
80 * 16 / 25 =
51.2 cm^2
Alternatively:
a1 / (s1^2) = a2 / (s2^2)
80 / 5^2 = x / 4^2
80 * 16 / 25 = x
51.2 = x
2007-08-16 13:01:21 · answer #1 · answered by McFate 7 · 0⤊ 0⤋
The new octagon results from a dilation of 4/5. So the area of the new octagon is .8^2*80 = 51.2 cm^2. This is true if the original octagon is a regular octagon or an irregular octagon.
2007-08-16 20:14:06 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
areas of similar plane figures are proportional t othe squares of the corresponding side:
A/80=4^2/5^2=16/25
A=16*80/25
=16*16/5
=256/5
51.2cm^2 ANS.
2007-08-16 20:12:17 · answer #3 · answered by Anonymous · 0⤊ 0⤋