Math Help - Trangle height formula?!

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

please help me find the height of the green triangle?!

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

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

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

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

Now, we focus our attention on triangle ABC.

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

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

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

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

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

Using similar triangles,

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

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

$AG = 33.18$

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