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

Lesson 5.7Surface Area of Triangular Prisms

Start hereWords, worked example, and sentence starters

Name Date Period

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

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 all 5 faces
Rectangular prismSpanish: Prisma rectangular A solid box shape with six flat rectangle sides. A box with 6 flat rectangle sides: top, bottom, front, back, left, right
Triangular prismSpanish: Prisma triangular A solid with two triangle ends and three flat rectangle sides. a tent shape
FaceSpanish: Cara One flat side of a solid shape. A triangular prism has 5 faces: 2 triangles + 3 rectangles
NetSpanish: Plantilla (desarrollo plano) A flat shape that folds up into a solid. Unfold a triangular prism flat: you see 2 triangles and 3 rectangles side by side
Lateral faceSpanish: Cara lateral The side faces of a solid, not the top or bottom. the 3 rectangles

How it worksWorked example

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

Prism 6 ft long; ends: base 8 ft, height 3 ft, sides 5 ft.

  1. Ends: 2 × (½ × 8 × 3) = 24 ft².
  2. Rectangles: (8 + 5 + 5) × 6 = 108 ft².
  3. Add: 24 + 108 = 132.

Answer: SA = 132 ft²

Say it and write itSentence starters

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

  • The net has triangles and rectangles.
  • Each triangular end has an area of square units.
  • Every rectangle uses as one of its sides.
  • The surface area is because I added .

Word bank triangular prismnetfacelateral facebasetrianglerectanglecongruentaddsurface areasquare unitslength

Watch out!A common mistake

A common mistake in Surface Area of Prisms is confusing surface area with volume

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

Lesson 5.7Surface Area of Triangular Prisms

Apply Day · Version ASupported practice

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

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

  1. 1Complete each step, then write the final answer.

    A rectangular prism is 6 in long, 2 in wide, and 1 in tall. Find its surface area.

    Show your work

    Hint Find each pair of matching faces. Then add.

    Final answer:
  2. 2Complete each step, then write the final answer.
    8 cm2 cm10 cm12 cm

    A triangular prism is 2 cm long. Each triangle end has a base of 12 cm and a height of 8 cm. The slanted sides are 10 cm. Find the surface area.

    Show your work

    Hint Find the 2 triangles. Then find the 3 rectangles. Add all 5 faces.

    Final answer:
  3. 3Complete each step, then write the final answer.

    A triangular prism is 3 in long. Its triangle ends have sides of 6 in, 8 in and 10 in. The 6 in and 8 in sides meet at a square corner. Find the surface area.

    Show your work

    Hint The sides at the square corner are the base and height of the triangle.

    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.4

Lesson 5.7Surface Area of Triangular Prisms

Apply Day · Version BCore practice

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

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

  1. 1Complete each step, then write the final answer.

    Rosa finds the surface area of a triangular prism. The rectangles are 12, 16 and 20 square inches. Each triangle end is 24 square inches. She adds 12 + 16 + 20 + 24 = 72. What is the correct surface area?

    Show your work
    Final answer:
  2. 2Complete 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:
  3. 3Complete each step, then write the final answer.

    A triangular prism is 3 cm long. Each triangle end has a base of 24 cm and a height of 5 cm. The slanted sides are 13 cm. Find the surface area.

    Show your work
    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.4

Lesson 5.7Surface Area of Triangular Prisms

Apply Day · ChallengeExtension

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

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

  1. 1Circle the letter of the best answer. Show how you know.

    A rectangular prism measures 6 cm long, 4 cm wide, and 2 cm tall. What is its surface area?

    1. A24 square centimeters
    2. B44 square centimeters
    3. C48 square centimeters
    4. D88 square centimeters
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  2. 2Complete 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:
  3. 3Complete each step, then write the final answer.

    A triangular prism is 6 in long. Its triangle ends have sides of 7 in, 24 in and 25 in. The 7 in and 24 in sides meet at a square corner. Find the surface area.

    Show your work
    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help