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Zyger · #11 May 19th, 2008, 06:49 PM

Quote:

Originally Posted by Mathstud28

Of course this is a site to learn

Ok so basically we have that $A=\frac{1}{2}a\cdot{p}$

where a is apothem and p is permieter

Now since we know that the exterior angle of a n-gon is $\frac{360}{n}$ we know due to the linear pair postulate that the interior angle of an n-gon is

$180-\frac{360}{n}$

so for a pentagon(5-gon)

the interior angle would be

$180-\frac{360}{5}=108$

So now we know that the angle at a vertex is 108 we know that the apothem bisects it making

the angle that the apothem cuts off 44...so now we have a right triangle with angles ,90,44,46

So we need to calculate the apothem or in this case we are given it but we need to find sidelenght

so we use trig $\sin(46)=\frac{x}{15}\Rightarrow{x=\sin(46)\cdot{15}\approx{10.875}}$

and since that gives us half of our side we see that the sidelenghts are

21.75

now we go to our formula

$A=\frac{1}{2}a\cdot{p}$

Now since $P_{pentagon}=5n$ where n is the sidelength we see that $A=5\cdot{21.75}=107.8$

so now we see

$A=\frac{1}{2}\cdot{107.8}\cdot{15}=808.75$

Thank you sooooooooooooooooooooooooooooooooo much