1. Trangle height formula?!

i need urgent help!!!

i need a formula for this question...

In this diagram, the area of a pentagon is 800 square centimeters.

What is the area of the green part, in square centimeters? Please round up to the nearest whole number, and submit only the answer.

i found the side length of the pentagon to be
21.56cm

2. Construct BE. Construct perpendicular bisector AC, extending it to D.

Now, $\displaystyle \angle BDE = \frac{180(5-2)}{5}=108^{\circ}$, and since triangle BDE is isoscles (BD = DE), we can conclude that $\displaystyle \angle EBD = \angle BED = \frac{1}{2}(180-108) = 36^{\circ}$
Now in triangle BCD,

$\displaystyle \cos{36^{\circ}}=\frac{BC}{21.5635622735}$

$\displaystyle \Rightarrow BC = 21.5635622735\cos{36^{\circ}}=17.4452883385$

Now, we focus our attention on triangle ABC.

$\displaystyle \angle ABC = 108 - 36 = 72^{\circ}$

Now, $\displaystyle \tan{72^{\circ}} = \frac{AC}{17.4452883385}$

$\displaystyle \Rightarrow AC = 17.4452883385\tan{72^{\circ}}=53.6910767207$

Also, $\displaystyle \cos{72^{\circ}}=\frac{17.4452883385}{AB}$

$\displaystyle \Rightarrow AB = \frac{17.4452883385}{\cos{72^{\circ}}} = 56.4541389505$

Using similar triangles,

$\displaystyle \frac{AB}{AF} = \frac{AC}{AG}$

$\displaystyle \frac{56.4541389505}{56.4541389505-21.5635622735}=\frac{53.6910767207}{AG}$

$\displaystyle AG = 33.18$

You can continue from here.

3. Haha, oh geeze, Soroban submitted a 3 line solution

4. Originally Posted by DivideBy0
Haha, oh geeze, Soroban submitted a 3 line solution
Where?

Ah! I see now.

@himachuu: Please don't double post. See rule #1 here.

-Dan