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!

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[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!