6.GR.4 Lesson 5-8-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.8 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Surface Area of Pyramids · Pyramid · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do we find the surface area of a pyramid?
1Surface area of a pyramid = base area + the area of all the 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. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me
  1. My square pyramid has a 6 in. × 6 in. base and a slant height of 8 in.
  2. First the base area: 6 × 6 = 36.
  3. Now one triangular face: ½ × 6 × 8 = 24. A square pyramid has 4 of them, so 4 × 24 = 96.
  4. I add the base and the side faces: 36 + 96 = 132.
  5. So the total surface area is 132 in². I used the slant height (8) for the triangles, not the pyramid's height.
3Mathematical Word Bank
  • Surface Area of Pyramids (Área de superficie de pirámides) — The total area of a pyramid's base and triangular faces. Formula: SA = B + lateral area.
  • Pyramid (Pirámide) — A solid with a flat bottom and triangle sides that meet at one point on top.
  • Slant height (Altura inclinada (apotema)) — The height of a side triangle, measured along its slanted face.
  • Lateral face (Cara lateral) — A triangle side of a pyramid, not the bottom.
  • Base (Base) — The flat bottom of a pyramid.
  • Apex (Ápice) — The point at the top of a pyramid where the sides meet.
4Watch out
  • A common mistake in Surface Area of Pyramids is finding the four triangular lateral faces correctly (½ × base edge × slant height, times 4) and then stopping — forgetting to add the base area at the end. This leaves the total surface area too small by exactly the base's area. Before you submit, ask: 'Did I add the base area to the four lateral faces, or did I stop after the sides?'
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A square pyramid has a base area of 49 cm² and a total lateral area of 84 cm². What is the surface area?

    1. A133 cm²
    2. B84 cm²
    3. C49 cm²
    4. D133 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?
  2. 2 MULTIPLE CHOICE

    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. A175 in²
    2. B126 in²
    3. C144 in²
    4. D175 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?
  3. 3 MULTIPLE CHOICE

    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. A20 in²
    2. B40 in²
    3. C13 in²
    4. D20 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. 4 MULTIPLE CHOICE

    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. A81 in²
    2. B36 in²
    3. C18 in²
    4. D324 in²
    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?
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Did You Halve the Triangle?

    1. 1Box:Square pyramid: base edge = 8 in, slant height = 10 in
    2. 2Base Area:8 × 8 = 64 in²
    3. 3One Triangular Face:8 × 10 = 80 in² (forgot the ½)
    4. 4Answer:SA = 64 + 4 × 80 = 64 + 320 = 384 in²

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Level 2 Extension — Slant Height vs. Base Edge

    1. 1Box:Square pyramid gift box: base edge = 12 in, slant height = 9 in
    2. 2Base Area:12 × 12 = 144 in²
    3. 3One Triangular Face:½ × 9 × 9 = 40.5 in² (used 9 for both numbers)
    4. 4Answer:SA = 144 + 4 × 40.5 = 144 + 162 = 306 in²

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It