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

Lesson 5.7Determine Surface Area of Prisms

Set B · Version ASecond form · supported practice

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

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

Why This Matters Your class is painting the outside of different time capsule shapes to protect them from weather. Some capsules are rectangular prisms and others are triangular prisms (wedge-shaped). To buy the right amount of paint, you need to calculate the surface area of each shape! One capsule is a rectangular prism 7 inches long, 4 inches wide, and 3 inches tall. Another is a triangular prism whose triangle bases are 8 inches wide and 3 inches tall, with slant sides of 5 inches, and the prism is 9 inches long.

RememberDetermine Surface Area of Prisms

Surface Area of Prisms. Formula: Surface Area = Sum of areas of all 6 faces Surface area is the total area of all the faces of a solid. A rectangular prism has 6 faces; a triangular prism has 5 faces (2 triangles + 3 rectangles). Add every face to get the total.

  1. Calculate area of Top & Bottom: 2 × (l · w).
  2. Calculate area of Front & Back: 2 × (l · h).
  3. Calculate area of Left & Right: 2 × (w · h), then sum all three pairs

Words: Surface area (Área de superficie)Rectangular prism (Prisma rectangular)Triangular prism (Prisma triangular)Face (Cara)Net (Plantilla (desarrollo plano))

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

    Surface area is measured in which type of unit?

    1. ACubic units (in³, cm³, ft³)
    2. BSquare units (in², cm², ft²)
    3. CLinear units (in, cm, ft)
    4. DNo units are needed
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    How many faces does a rectangular prism have?

    1. A4
    2. B6
    3. C8
    4. D12
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    A net of a rectangular prism shows six rectangles with areas 12, 12, 18, 18, 24 and 24 square inches. What is the surface area?

    1. A54 in²
    2. B72 in²
    3. C108 in²
    4. D108 in³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  4. 4Circle the letter of the best answer. Show how you know.

    A net for a triangular prism has how many triangles and how many rectangles?

    1. A1 triangle and 4 rectangles
    2. B2 triangles and 3 rectangles
    3. C2 triangles and 4 rectangles
    4. D3 triangles and 2 rectangles
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A carpenter builds wooden storage chests. A rectangular chest is 3 feet long, 2 feet wide, and 2 feet tall. Wood stain covers 50 square feet per can. What is the chest's surface area?

    1. A12 ft²
    2. B16 ft²
    3. C24 ft²
    4. D32 ft²
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  6. 6Circle the letter of the best answer. Show how you know.

    A carpenter builds wooden storage chests. A rectangular chest is 3 feet long, 2 feet wide, and 2 feet tall. Wood stain covers 50 square feet per can. How many cans of stain are needed for one chest?

    1. A0
    2. B1
    3. C2
    4. D3
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?

Explain your thinkingCompare Capsule A (rectangular, SA = 248 in²) and Capsule C (triangular, SA = 184 in²). Even though they are similar in size, why does the rectangular prism need more paint?

Sentence starter The rectangular prism has ___ faces while the triangular prism has ___ faces. The rectangular prism's SA is ___ in² which is ___ more than the triangular prism's ___ in² because ___.

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 5.7Determine Surface Area of Prisms

Set B · Version BSecond form · core practice

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

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

Why This Matters Your class is painting the outside of different time capsule shapes to protect them from weather. Some capsules are rectangular prisms and others are triangular prisms (wedge-shaped). To buy the right amount of paint, you need to calculate the surface area of each shape! One capsule is a rectangular prism 7 inches long, 4 inches wide, and 3 inches tall. Another is a triangular prism whose triangle bases are 8 inches wide and 3 inches tall, with slant sides of 5 inches, and the prism is 9 inches long.

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Find each prism's surface area. Then sort it by whether it needs 96 in² of paper or less, or more than 96 in².

    Groups: 96 in² of paper or less More than 96 in²
    • Rect capsule 3×4×5
    • Cube capsule 4×4×4
    • Rect capsule 6×5×4
    • Tri capsule (ends 8×6, length 10)
  2. 2Write the letter of the matching item on each line.

    Match each rectangular capsule's dimensions to how much cardboard wraps its surface.

    1. 7 in × 3 in × 2 in
    2. 6 in × 4 in × 2 in
    3. 9 in × 2 in × 2 in
    4. 6 in × 5 in × 3 in
    • A82 in²
    • B88 in²
    • C80 in²
    • D126 in²
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A carpenter builds wooden storage chests. A rectangular chest is 3 feet long, 2 feet wide, and 2 feet tall. Wood stain covers 50 square feet per can. The carpenter builds a second identical chest. Now how many cans?

    1. A1
    2. B2
    3. C3
    4. D4
    per 1
  2. 4Circle the letter of the best answer. Show how you know.

    A rectangular time capsule box measures 3 in by 4 in by 5 in. How much wrapping paper covers its surface (no overlap)?

    1. A47 in²
    2. B60 in²
    3. C94 in²
    4. D94 in³
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    A rectangular capsule crate is 6 cm long, 5 cm wide, and 4 cm tall. How much cardboard is needed to cover all its faces?

    1. A74 cm²
    2. B120 cm²
    3. C148 cm²
    4. D148 cm³
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    A triangular prism is 10 in long. Its triangle ends have base 8 in, height 6 in, and sides 8, 6, and 10 in. Find its surface area.

    1. A48 in²
    2. B240 in²
    3. C288 in²
    4. D288 in³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit

Explain your thinkingCompare Capsule A (rectangular, SA = 248 in²) and Capsule C (triangular, SA = 184 in²). Even though they are similar in size, why does the rectangular prism need more paint?

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