# Polygon Bowl

Geometry Level 5

Four regular hexagons with side length $$22$$ are attached by their sides to a square, also with side length $$22$$. The hexagons are then folded upwards to create a bowl. From base to rim, the height of this bowl can be expressed as $$\sqrt{a}$$, where $$a$$ is a positive integer. Find the value of $$a$$.

Details and assumptions

From base to rim is the height of the bowl normal to the base, i.e straight up and down.

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