Geometry // Prismatic Study

Volume of Triangular Prisms

From Divided Rhombus to Mathematical Formula

Material Analysis

Divided rhombus pieces (triangular prisms), tickets, labels, ruler.

Presentation: The Transformation

Hold up two triangular prisms from the divided rhombus. Prove equivalence.

"Can we transform this triangular shape into a rectangle? Watch—we haven't changed the volume, only the appearance. The base of our new rectangle is exactly half the base of our triangle."

FIG 1.1: TRANSFORMING TRIANGLE TO RECTANGLE

"We know the area of a triangle is $(base \times height) \div 2$. To find the volume of the whole prism, we simply multiply that base area by the prism's height."

Volume = $(\frac{b \times h}{2}) \times Prism\_Height$

"Remind the child: The height of the triangle (face) is different from the height of the prism (length). Using different colored pencils for each helps avoid confusion."