geometry help!! area of polygons..

[CJS525]

i really dont understand this... if someone could explain it, that'd be amazing.. i've got 3 problems to show what i need help with.. thanks!

[/img][/url][/quote]

 

[happy]

What are the complete instructions?

 

[CJS525]

find the apothem, side legnth, perimeter and area. thats all, i hope that helps!

 

[soroban]

Hello, CJS525!

I assume these are all regular polygons
$\displaystyle \;\;$and that the interior point is the "center" of the figure.

Here's a start . . .

                  *
                 / \
                /   \
               /     \
              /       \
             /         \
            /           \
           /      B      \
          /       *       \
         /  8  *  |        \
        /   *     |         \
       / * 30°    |          \
     A* - - - - - + - - - - - *
                  C

In right triangle $\displaystyle ABC$, we have: $\displaystyle \,\angle BAC\,=\,30^o,\;AB\,=\,8$
Hence: $\displaystyle \,BC\,=\,4,\;AC = 4\sqrt{3}$

$\displaystyle S\:=\:8\sqrt{3}$

$\displaystyle a\:=\:4$

$\displaystyle P\:=\:3\,\times 8\sqrt{3}\:=\:24\sqrt{3}$

$\displaystyle A\:=\:\frac{\sqrt{3}}{4}S^2\:=\:48\sqrt{3}$

 

[CJS525]

awesome... thanks so much! i've got a test on this tomorrow... thanks!