The side lengths of an equiangular octagon are $1$, $2$, $3$, $4$, $1$, $2$, $3$, and $4$ in clockwise order. Find the octagon's area.
I don't know how to do this.
Ms.Sue, just ignore the dollar signs
Reiny, when its equilangular the angles are indeed equal but that doesn't mean the sides are also equal. ( That's regular)
To find the area of the equiangular octagon, we can use the formula for the area of a regular octagon, which is given by
\[A = 2(1+\sqrt{2})s^2,\]
where $A$ is the area and $s$ is the side length.
In this problem, we are given the side lengths of the octagon as $1$, $2$, $3$, $4$, $1$, $2$, $3$, and $4$ in clockwise order. To find the area, we need to find the length of one side of the octagon.
We can see that the pattern of the side lengths is $1$, $2$, $3$, $4$, $1$, $2$, $3$, and $4$. Since the octagon is equiangular, we can determine that the side length of the octagon is $2$, as the side lengths repeat in the pattern $1$, $2$, $3$, $4$.
Now that we have the value of the side length ($s = 2$), we can substitute it into the formula for the area of the octagon:
\[A = 2(1+\sqrt{2})(2^2).\]
Evaluating the expression inside the parentheses gives us
\[1+\sqrt{2} = 1+1.41 = 2.41.\]
Substituting this value into the formula, we have
\[A = 2(2.41)(4) = 19.28.\]
Therefore, the area of the equiangular octagon is $19.28$ square units.
Mrs Sue thats what happens when someone copy and pastes a problem directly from some website. Those dollar signs when pasted into a console make the text regular, into times new roman font, and is boded.
What do the dollar signs ($) mean?
This makes no sense to me.
If the octagon is equiangular (all angles are equal) , how can the side be of different lengths ?