Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.4

Lesson 5.75.7 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the surface area of rectangular and triangular prisms, explain why the method works, and use it on a problem I have not seen before.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Surface areaSpanish: Área de superficie The total area of all the flat sides of a solid. add every face
Rectangular prismSpanish: Prisma rectangular A solid box shape with six flat rectangle sides. 3 congruent pairs
Triangular prismSpanish: Prisma triangular A solid with two triangle ends and three flat rectangle sides. Shaped like a tent or a wedge of cheese — 2 triangle ends + 3 rectangle sides
FaceSpanish: Cara One flat side of a solid shape. top, side, end
NetSpanish: Plantilla (desarrollo plano) A flat shape that folds up into a solid. unfolded box
Lateral faceSpanish: Cara lateral The side faces of a solid, not the top or bottom. On a triangular prism, the 3 rectangles that wrap around the sides are lateral faces

How it worksWorked examplesurface area from a net

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A rectangular prism is 9 cm long, 6 cm wide, and 4 cm tall. Find its surface area.

  1. Unfold it into a net. The 6 faces come in 3 matching pairs.
  2. Find one face from each pair. 9 × 6 = 54 9 × 4 = 36 6 × 4 = 24
  3. Add those three. 54 + 36 + 24 = 114
  4. Each one happens twice, so double. 114 × 2 = 228

Answer: The surface area is 228 square centimeters (228 cm²).

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A rectangular prism is 11 in. long, 8 in. wide, and 2 in. tall. Find its surface area.

  1. Sketch the net. How many faces, and how many pairs? ,
  2. One face from each pair: × = · × =
  3. Third face and sum: × = Total of the three:
  4. Double it. × 2 = in²
Answer:surface area of the prism

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The prism has faces in matching pairs.
  • The three different face areas are , , and .
  • I doubled each face area because .
  • The surface area is square units.

Word bank surface areanetfacecongruentpairprismunfoldadddoublesquare unitstopside

Watch outA common mistake

A common mistake in Surface Area of Prisms is confusing surface area with volume — multiplying l × w × h (which finds the space INSIDE the prism, in cubic units) instead of adding the areas of all the faces (SA = 2lw + 2lh + 2wh, in square units). A second common slip is forgetting to double one face pair, like writing 2(l×w) + 2(l×h) + (w×h) instead of + 2(w×h) — always count all 6 faces (or all 5 for a triangular prism) before you submit.

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.4

Lesson 5.75.7 Small Group · Group 2

Group 2Challenge practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the surface area of rectangular and triangular prisms, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    3 in12 in16 in20 in

    A triangular prism is 3 in long. Its triangle ends have sides of 12 in, 16 in and 20 in. The 12 in and 16 in sides meet at a square corner. Find the surface area.

    1. 1Which sides are the base and height of the triangle?
    2. 2What is the area of both triangle ends?
    3. 3Use perimeter × length for the three rectangles. What do you get?
    4. 4What is the surface area?
    Final answer:
  2. 2Complete each step, then write the final answer.
    ? in6 in8 in10 in

    A triangular prism has right-triangle ends with sides of 6 in, 8 in and 10 in. Its surface area is 216 square inches. How long is the prism?

    1. 1What is the area of both triangle ends?
    2. 2How much area is left for the three rectangles?
    3. 3The triangle's perimeter is 24 in. How long is the prism?
    4. 4Why can you divide 168 by the perimeter, 24?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A triangular prism is 2.5 cm long. Each triangle end has a base of 16 cm and a height of 15 cm. The slanted sides are 17 cm. Find the surface area.

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Dev finds the surface area of a box 6 in by 4 in by 3 in with a shortcut: (6 + 4 + 6 + 4) × 3 = 60. He stops there. What is the real surface area?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A gift box is a triangular prism 10 in long. Each end is a triangle with three 6 in sides and a height of 5.2 in. How much paper covers the box?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    A prism is 2 cm long. Its right-triangle ends have sides of 9 cm, 12 cm and 15 cm, with the square corner between 9 cm and 12 cm. Mo uses 1/2 × 12 × 15 for each end. Find the correct surface area.

    Show your work
    Final answer:

Explain your thinkingIn a right triangle, which sides give the triangle's area? Which sides make the rectangles? Use Mo's mistake to explain.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help