A strange octagon

Geometry Level 5

ABCD is a square with a side length of \( 3 \sqrt{3} \). AED, DGC, AHB and BFC are equilateral triangles.
The area of the polygon IJKLMNOP is \(a + b \sqrt{3} \), where \(a\) and \(b\) are rational numbers.
What is the value of \(a+b\)?

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Marius Munteanu by Marius Munteanu
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