# Triangle-Ception IV

Geometry Level 5

In the diagram above, $$OAD$$ is a quarter circle of radius 2.$$OB$$ and $$OC$$ trisect arc $$AD$$, and $$DE$$ bisects segment $$OA$$. If the area of quadrilateral $$WXYZ$$ can be expressed in the form

$\dfrac{m}{n}(p-q\sqrt{r})$

for positive integers $$m,n,p,q$$ and $$r$$ with $$\gcd(m,n)=1$$, $$\gcd(p,q)=1$$, and $$r$$ is not divisible by the square of any prime. Find the value of

$m+n+p+q+r.$

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