Represent three-dimensional figures using nets

What you'll learn

1. Identify a rectangular prism, triangular prism, square pyramid, or triangular pyramid by counting faces, edges, and vertices, and naming face shapes.
2. Unfold a 3D figure into a net of rectangles and triangles, and recognize that different unfoldings produce different (but equally valid) nets.
3. Decide whether a candidate flat arrangement of polygons is a valid net for a given 3D figure by checking face count, face shapes, and how faces fold together.
4. Compute the surface area of a rectangular prism by summing the areas of its 6 rectangular faces, equivalently SA = 2(lw + lh + wh).
5. Compute the surface area of a triangular prism by summing 2 triangular face areas + 3 rectangular face areas, equivalently SA = 2B + (perimeter of base)(prism height).
6. Compute the surface area of a square pyramid (1 square + 4 triangles) and a triangular pyramid (4 triangles), using the slant height of each triangular face.
7. Solve real-world surface area problems (wrapping, painting, packaging, tent canvas), recognizing that some problems include all faces and others exclude specific faces.

Prerequisites

• Find the area of right triangles, other triangles, special quadrilaterals, and polygons