Lesson 3: Properties of 3D Figures: Prisms and Pyramids

Property

Polyhedra are split into two main families based on how they are built:

• Prism: A 3D figure with 2 parallel, congruent polygons as bases. The lateral faces connecting the bases are flat rectangles or parallelograms.
• Pyramid: A 3D figure with exactly 1 polygon base. All other flat faces are triangles that connect to a single point at the top called the apex.

Examples

• A rectangular prism (like a shoebox) has 2 rectangular bases and 4 rectangular lateral faces.
• A triangular prism, like a tent, has 2 triangular faces as bases and 3 rectangular faces as sides.
• A square pyramid has one square base and four triangular faces that meet at the top apex.

Explanation

Prisms are like shapes that have been 'stretched' straight up; whatever shape is on the bottom floor matches the top ceiling exactly. Pyramids only have a bottom floor, and their walls lean inward to meet at a single sharp point at the very top.

Property

Volume is the measure of how much 3D space is inside an object, or how much it takes to fill a container.

• Volume is always measured in cubic units (like cubic inches, cubic cm, or cubic meters).
• In any prism, the Base (Big B) is the area of the geometric shape that forms the top and bottom. The height (h) is the straight, perpendicular distance between those two identical Bases.

Examples

• To find how much soil is needed to fill a rectangular planter box, you calculate the Volume in cubic feet.
• Identifying the Base: In a triangular prism, the "Base" isn't the flat rectangle it sits on; the "Bases" are the two identical triangles on the ends! The height is the distance connecting those two triangles.

Explanation

Think of Volume like filling a pool with water or packing a box with tiny 1x1x1 cubes. Because we are measuring in 3D (length, width, and depth), our answers must always wear a "cubic" badge! The secret to mastering volume is learning to spot the "Big B" (the area of the base shape). Once you find the Big B, the rest is easy.