The general shape of a cell would be a cirle, or an oval
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A general quadrilateral. No special name.
With 2 acute and 2 obtuse angles it has 4 angles - the shape is a quadrilateral. The shape can be one of trapezium, parallelogram, rhombus, kite or a general quadrilateral. With the two acute angles next to each other (forcing the two obtuse angles to be next to each other) the shape can be either a trapezium or a general quadrilateral.
A general trapezium, and selected versions of polygons with 5 or more sides.
Depends on the shape of the room. For a rectangular floor area, it is lengthxwidthxheight. In general find the floor area and multiply by the height, assuming a flat ceiling of constant height.
The general convention for polygons with large numbers of sides is to simply put the number of side followed by the suffix -gon. In this case, it would be a 600-gon.