Area of an Octagon

[vampirewitchreine]

Hi again,
I know that this is probably a really dumb question, but how do I find the area of an octagon if the only length that is provided is the length of the sides?

My problem:
Two regular octagons have sides that are 8 in. and 9 in. respectively. What is the ratio of the corresponding diagonals?


Also, by knowing the area will this help me to determine the information that I need? (Again, probably a really dumb question, but I'm asking anyway)

 

[tkhunny]

Hi again,
I know that this is probably a really dumb question, but how do I find the area of an octagon if the only length that is provided is the length of the sides?

You don't. There are too many octagons. You must find a specific octagon.

My problem:
Two regular octagons have sides that are 8 in. and 9 in. respectively. What is the ratio of the corresponding diagonals?

1) That word "regular" is VERY important. This narrows down the field of octagons to a unique candidate. NOW we can calculate the area.
2) However, that is not the question. We just need the ratio. Let's experiment with a line and a square.

What is the ratio of the lengths of two line segments, one measuring 8 and the other 9? Answer this, please.
What is the ratio of the areas of two squares, one measuring 8 on a side and the other 9 on a side? Answer this, please.

The answers to these two questions can lead you to your solution WITHOUT calculating the area or the length of the diagonal.

 

[vampirewitchreine]

What is the ratio of the lengths of two line segments, one measuring 8 and the other 9? Answer this, please.

8:9

What is the ratio of the areas of two squares, one measuring 8 on a side and the other 9 on a side? Answer this, please.

Well 8*8= 64
and 9*9= 81

Since there's no number that can evenly divide both numbers the ratio is 64:81

 

[tkhunny]

Okay, now answer the question. What is the ratio of the diagonals (or any other linear measurement)?

While you're at it, what is the ratio of the areas (or any other 2D measurement)?