# a hard pentagon questionABCDE

#### kastamonu

ABCDE is a regular pentagon.CF is perpendicular to AB. KL is perpendicular to AC. |FB|=|KL|.|DE|=6 units. Find area of triangle AKC?
https://postimg.org/image/8yw954k9z/

Question and image are very clear. I don't want any solution with trigonometry and golden ratio. I don't want to hear any comment about my drawing. If you know the answer you are wellcome.

#### chiro

MHF Helper
Hey kastamonu.

We ask that people put in their own attempts before giving further guidance.

#### yeongil

You've already asked this question about six months ago here. I'm wondering why is it necessary to solve this without trig or use of the golden ratio.

01

#### kastamonu

I solved it without trig. but if there is another way I would like to learn.

#### kastamonu

This is my solution with golden:
In triangle BCA AC=6phi(GOLDEN RATIO)
In triangle FBC LET FB be X
sin18=1/2phi
x/6=1/2phi
X=6/2phi
area is AC.KL/2
AC=6phi
KL=6/2phi
6phi.6/2phi divided by 2=9
If you have a solution ignoring trig or golden you are wellcome.

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