6.GR.4 Lesson 5-8-part2 Apply Day · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.8 · Part II

Second Practice Form · Independent Application and Spiral Review

Surface Area of Pyramids · Pyramid

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 5.8 · Part II
1Surface Area of Pyramids
2The Structural Procedure
  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
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 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
  2. 2 MULTIPLE CHOICE

    A square pyramid has a base edge of 5 in and a slant height of 7 in. What is the surface area?

    1. A95 in²
    2. B70 in²
    3. C95 in³
    4. D120 in²
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  3. 3 MULTIPLE CHOICE

    How many lateral (triangular) faces does a square pyramid have?

    1. A4
    2. B3
    3. C5
    4. D6
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    What is the area of one triangular face with base 8 in and slant height 6 in?

    1. A24 in²
    2. B48 in²
    3. C14 in²
    4. D24 in³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 OPEN RESPONSE

    Two pyramids have the same base area (64 in²) but different slant heights. Pyramid A has slant height 6 in and Pyramid B has slant height 10 in. How much more surface area does Pyramid B have? Why does slant height affect surface area but NOT base area?

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

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

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It