Grade 6 (age 11-12)

Prisms and Pyramids

Prisms and pyramids are solid figures you see all around you. A prism has two identical bases and rectangular sides, like a milk carton, while a pyramid has one base and a pointed top with triangular sides, like an Egyptian pyramid. The number of base sides, n, sets how many vertices, edges, and faces there are, so here you change n and rotate the figure to explore both shapes and their nets.

What are 3D Figures?

📦 2D vs 3D Figures

①2D: flat shapes drawn on paper (triangle, square)

②3D: solid figures occupying space (box, pyramid)

③3D figures have faces, edges, and vertices

④Prisms and pyramids are common 3D figures!

Exploring Prisms

🏛️ What Does a Prism Look Like?

①Same-shaped polygons (bases) on top and bottom

②All side faces are rectangles

③Prism, milk carton, triangular ruler case are prisms

Sides of base (n)4

Rotation0°

Exploring Pyramids

🔺 What Does a Pyramid Look Like?

①Only one base; tip is pointed

②All side faces are triangles

③Egyptian pyramid is a square pyramid!

④Triangular, square, pentagonal pyramids by base shape

Nets

✂️ What is a Net?

①A 3D figure cut and unfolded

②Prism: 2 bases + n side rectangles

③Pyramid: 1 base + n side triangles

④Folding a net gives back the 3D figure!

Summary

Prism (n-gon prism)

Vertices = 2n, Edges = 3n, Faces = n + 2

2 bases (n-gon) + n side rectangles

Pyramid (n-gon pyramid)

Vertices = n + 1, Edges = 2n, Faces = n + 1

1 base (n-gon) + n triangle sides + apex

Prism vs Pyramid

Prism: 2 bases (congruent) / Pyramid: 1 base + apex

Prism sides are rectangles; pyramid sides are triangles

🎯 Key Points

①Prism: same top/bottom bases, side faces rectangles

②Pyramid: 1 base, pointed apex, side faces triangles

③Larger n → more vertices/edges/faces

④Prism faces = n+2; pyramid faces = n+1

⑤Folding a net builds the 3D figure!

Examples & Unit Review

Example 1

Find the numbers of vertices, edges, and faces of a pentagonal prism.

An n-gon prism has vertices = 2n, edges = 3n, faces = n + 2. For a pentagonal prism, n = 5.

Vertices = 2 × 5 = 10, edges = 3 × 5 = 15, faces = 5 + 2 = 7.

▸ Vertices 10, edges 15, faces 7

A prism has 2 bases and n rectangular side faces, so it has n + 2 faces.

Example 2

Find the numbers of vertices, edges, and faces of a hexagonal pyramid.

An n-gon pyramid has vertices = n + 1, edges = 2n, faces = n + 1. For a hexagonal pyramid, n = 6.

Vertices = 6 + 1 = 7, edges = 2 × 6 = 12, faces = 6 + 1 = 7.

▸ Vertices 7, edges 12, faces 7

A pyramid has 1 base, n triangular side faces, and 1 apex vertex.

Unit Review

How many edges does a triangular prism have in total?

①9

②6

③12

④5

▸ ① 9

An n-gon prism has 3n edges. For a triangular prism, n = 3.

3 × 3 = 9, so it has 9 edges.

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