Lesson 6: Represent Three-Dimensional Figures in Two Dimensions6.GR.4

I can…

I can find the surface area of a solid by using its net.

Key words

• Surface Area Using Nets — Unfold the solid. Then add up every face.
• Surface area — The area of all the flat sides added together.
• Net — A flat shape that folds into a solid.
• Face — One flat side of a solid shape.
• Two-dimensional — A flat shape with length and width, but no thickness.
• Edge — Where two flat sides of a solid meet.
• Pyramid — A solid with a flat bottom and triangles that meet on top.
• Vertex — A corner where edges or sides meet.

Steps

1. My box is 8 in. long, 5 in. wide, and 3 in. tall. I unfold it into a net and see 3 pairs of faces.
2. Top and bottom: each is 8 × 5 = 40, and there are 2 of them, so 2 × 40 = 80.
3. Front and back: each is 8 × 3 = 24, so 2 × 24 = 48.
4. Left and right: each is 5 × 3 = 15, so 2 × 15 = 30.
5. I add all the pairs: 80 + 48 + 30 = 158. The surface area is 158 in².

Try it

You wrap a shoebox as a birthday gift. The box has l = 10 in, w = 5 in, h = 2 in. How much wrapping paper covers it exactly (its surface area)?

Check your answer

160 in²

SA = 2(10×5) + 2(10×2) + 2(5×2) = 100 + 40 + 20 = 160 in². Surface area uses square units (in²).

Sentence starter

I know ___ because ___.

Goal: I can explain my work using the words surface area, net, face, and two-dimensional.