Geometry // Volume Narrative Step 7

Hexagonal Prisms

The Accumulation of Sides and Apothems

Material Analysis

Divided hexagonal prism (standard 3-part or 4-part division), apothem tickets, side length markers, pencil and paper.

Presentation: Building the Long Rectangle

Take the pieces of the divided hexagon and line them up to form one long rectangular prism.
"We are going to find the area of this base first. Look at this long side. It is made of three halves of a hexagon side ($1.5s$). And the height of our base? It is exactly two apothems ($2a$)."
BASE = 1.5 × SIDE HT = 2 × APOTHEM
FIG 7.1: RECONFIGURING HEXAGON PIECES
"When we simplify this, we see that the base area is the same as $(\frac{Perimeter \times Apothem}{2})$. Now, we just multiply that by the overall height of the prism to find the total volume."
Volume = $(\frac{P \times a}{2}) \times h$
"Some hexagonal prisms in the classroom are divided into four pieces rather than three. Encourage the children to sketch exactly what they see in their hands—the math remains identical!"