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.
by
Daniel Liu