Consider the pentagon below. Find its area.
Problem
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Tags: geometry, pentagon, area
natmath
31.12.2020 10:58
Starting from the right angle, the vertices are labelled in CC order as $ABCDE$
Draw segments $BE$ and $BD$
$BD=\sqrt{3}$ by LOC, so $\angle DBC=30$
This means $\angle EBD=75$
So $[ABCDE]=[ABE]+[BCD]+[EBD]=\frac{1}{2}+\frac{\sqrt{3}}{2}+\frac{\sqrt{6}}{2}\sin 75$
$=\frac{5+3\sqrt{3}}{2}$
HamstPan38825
31.12.2020 18:59
Pretty simple by splitting the thing up. natmath you should sleep if I presume you are in the correct timezone