Question 591961: Hi! I need help on finding the area and apothem of a quadrilateral. The radius is 8sqrt2. Im sorry if that is not enough of information.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
In order to be certain that your quadrilateral actually has an apothem, then it must be a regular quadrilateral, in other words, a square. I'm also presuming that  is the circumradius, i.e. the distance from the center of the square to any vertex. Given those assumptions, the apothem of a regular  -gon is found by:
)
where  is the circumradius and is the number of sides.
Now that you know both the circumradius and the inradius (same thing as the apothem) you have two methods to compute the area of a regular -gon:
Using the circumradius,  :
}{2})
Using the inradius (apothem),  :
)
Just plug in your values and do the arithmetic.
Hint: \ =\ \sin(45^\circ)\ =\ \frac{\sqrt{2}}{2}) , \ =\ 1) , and \ =\ 1)
John
My calculator said it, I believe it, that settles it
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