G.GMD.A.3 STUDENT NOTES WS #1/#2 – geometrycommoncore1

THE PRISM
A prism is a polyhedron that consists of a polygonal region and its translated image in a parallel plane, with quadrilateral faces connecting the corresponding edges.
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A common misconception is that whatever face the prism is ‘sitting’ on is the base – that IS NOT HOW THE BASE IS DETERMINED!! The base represents the two congruent opposite parallel faces. The height of the prism is the perpendicular distance between the two congruent bases.
The stacking of congruent parallel cross sections allows us to create a formula for the volume of prism.

VolumePRISM = Bh, where B is the area of the base and h is the height of the prism.

PRISM VOLUME CALCULATION

The formula for the volume of a prism is quite simple. The capital B represents the AREA of the base. This sometimes confuses students because they might use the base of a triangle or the base of a trapezoid here instead of the AREA of the base. It is for this reason that this B has been capitalized to distinguish it different from b or b1. The height, h, refers to the height of the prism which is one of the lateral sides if it is a right prism. This too is sometimes confusing because bases will have heights as well. /
Example #1 / Example #2 / Example #3
Name: Cube / Name: Triangular Prism / Name: Rectangular Prism
V = Bh
V = (Area of Square)(height)
V = (5)(5) (5)
V = 125 cm3 / V = Bh
V = (Area of Triangle)(height)
V = ½ (5)(8) (10)
V = 200 cm3 / V = Bh
V = (Area of Rectangle)(height)
V = (3)(4) (12)
V = 144 cm3
Example #4
Name: Hexagonal Prism
Example #5