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

Lesson 5.8Determine Surface Area of Pyramids

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 a pyramid by adding the base area and the lateral faces.

Why This Matters Your class is building a pyramid-shaped display to showcase the time capsule at the school entrance. The pyramid will be covered in gold leaf to make it shine. To figure out how much gold leaf you need, you must calculate the total surface area — the base plus all the triangular faces! The pyramid has a square base that is 10 inches on each side, and each triangular face has a slant height of 12 inches.

RememberDetermine Surface Area of Pyramids

Surface Area of Pyramids. Formula: Surface Area = Base Area + Sum of Triangular Lateral Faces Surface area of a pyramid is the base area plus all the triangular side faces. A square pyramid has 1 square base and 4 triangular faces. Each triangle uses the slant height: ½ × base × slant height.

  1. Calculate area of base polygon (square, rectangle, or triangle).
  2. Calculate area of each triangular face using ½ × base × slant height.
  3. Add the base area and all triangular face areas together

Words: Pyramid (Pirámide)Slant height (Altura inclinada (apotema))Lateral face (Cara lateral)Base (Base)Apex (Ápice)

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

    How many faces does a triangular prism have?

    1. A3
    2. B4
    3. C5
    4. D6
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    A prism's faces have areas 10 cm², 10 cm², 6 cm², 6 cm², 15 cm² and 15 cm². What is the surface area?

    1. A31 cm²
    2. B52 cm²
    3. C62 cm²
    4. D62 cm³
    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?
  3. 3Circle the letter of the best answer. Show how you know.

    A triangular prism has two triangular bases each with area 12 cm² and three rectangular faces with areas 30 cm², 40 cm², and 40 cm². What is the total surface area?

    1. A110 cm²
    2. B122 cm²
    3. C134 cm²
    4. D134 cm³
    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.

    What is the surface area of a rectangular prism with l = 5 cm, w = 4 cm, h = 3 cm?

    1. A47 cm²
    2. B60 cm²
    3. C94 cm²
    4. D94 cm³
    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?
  5. 5Circle the letter of the best answer. Show how you know.

    A museum is building a square pyramid display case. The base edge is 3 feet and the slant height is 4 feet. The glass costs $12 per square foot. What is the area of one triangular face?

    1. A3 ft²
    2. B6 ft²
    3. C7 ft²
    4. D12 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 museum is building a square pyramid display case. The base edge is 3 feet and the slant height is 4 feet. The glass costs $12 per square foot. What is the total glass area for all four faces?

    1. A12 ft²
    2. B24 ft²
    3. C30 ft²
    4. D33 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?

Explain your thinkingDisplay B has the largest surface area (280 in²). What contributes more to the total — the base or the lateral faces? Why?

Sentence starter For Display B, the base area is ___ in² and the total lateral area is 4 × ___ = ___ in². The ___ contribute(s) more 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 5.8Determine Surface Area of Pyramids

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 a pyramid by adding the base area and the lateral faces.

Why This Matters Your class is building a pyramid-shaped display to showcase the time capsule at the school entrance. The pyramid will be covered in gold leaf to make it shine. To figure out how much gold leaf you need, you must calculate the total surface area — the base plus all the triangular faces! The pyramid has a square base that is 10 inches on each side, and each triangular face has a slant height of 12 inches.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each square-pyramid gift box (base edge × slant height) to its total surface area.

    1. Base 5 in, slant 8 in
    2. Base 6 in, slant 7 in
    3. Base 8 in, slant 9 in
    4. Base 10 in, slant 6 in
    • A105 in²
    • B120 in²
    • C208 in²
    • D220 in²
  2. 2Write the name of the correct group on each line.

    A gift box can be a square pyramid (4 triangle faces) or a rectangular pyramid (a rectangle base with 4 triangle faces). Sort each measurement into the box part it describes.

    Groups: Base (bottom) Triangular faces
    • Square: side × side
    • Rectangle: length × width
    • ½ × base edge × slant height
    • Uses the slant height as its height
    • Add 4 of these together
    • Only one of these on the box
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A museum is building a square pyramid display case. The base edge is 3 feet and the slant height is 4 feet. The glass costs $12 per square foot. What will the glass cost?

    1. A$72
    2. B$144
    3. C$288
    4. D$396
    per 1
  2. 4Circle the letter of the best answer. Show how you know.

    Your first gift box is a square pyramid with a base edge of 7 in and a slant height of 9 in. How much wrapping paper (total surface area) covers it?

    1. A126 in²
    2. B144 in²
    3. C175 in²
    4. D175 in³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  3. 5Circle the letter of the best answer. Show how you know.

    Before adding the base, you need the area of just one triangular face of a gift box with base edge 8 in and slant height 5 in. What is it?

    1. A13 in²
    2. B20 in²
    3. C20 in³
    4. D40 in²
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  4. 6Circle the letter of the best answer. Show how you know.

    A gift box is a square pyramid with a base edge of 9 in. What is the area of its square base (the part that sits on the table)?

    1. A18 in²
    2. B36 in²
    3. C81 in²
    4. D324 in²
    Formula
    Put the numbers in
    Work it out
    Answer with its unit

Explain your thinkingDisplay B has the largest surface area (280 in²). What contributes more to the total — the base or the lateral faces? Why?

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