Lesson 7: Determine Surface Area of Prisms6.GR.4

I can…

I can find the surface area of rectangular and triangular prisms.

Key words

• Surface Area of Prisms — Add the area of every face of a prism.
• Surface area — The area of all the flat sides added together.
• Rectangular prism — A box shape with six flat sides.
• Triangular prism — A solid with two triangle ends and three flat sides.
• Face — One flat side of a solid shape.
• Net — A flat shape that folds into a solid.
• Lateral face — A side face of a solid, not the top or bottom.
• Congruent — Exactly the same size and shape.

Steps

1. My triangular prism has triangle bases (base 6 in., height 4 in.), is 10 in. long, and the two slant sides are 5 in. each.
2. Each triangle base is ½ × 6 × 4 = 12, and there are 2 of them: 2 × 12 = 24.
3. Now the 3 rectangles: 6 × 10 = 60, 5 × 10 = 50, and 5 × 10 = 50, which add to 160.
4. I add the bases and the rectangles: 24 + 160 = 184.
5. So the surface area is 184 in². I counted 5 faces because it is a triangular prism.

Try it

You are painting every outside face of a toy chest at home. It is l = 5 ft, w = 4 ft, h = 2 ft. How many square feet will you paint (its surface area)?

Check your answer

76 ft²

SA = 2(5×4) + 2(5×2) + 2(4×2) = 40 + 20 + 16 = 76 ft². Surface area uses square units (ft²).

Sentence starter

I know ___ because ___.

Goal: I can explain my work using the words surface area, rectangular prism, triangular prism, and face.