Learn on PengiBig Ideas Math, Advanced 1Chapter 8: Surface Area and Volume

Lesson 3: Surface Areas of Pyramids

In this Grade 6 lesson from Big Ideas Math Advanced 1, students learn how to find the surface area of square pyramids and triangular pyramids using nets. They identify base faces and lateral faces, then calculate surface area by summing the areas of the square or triangular base and each triangular lateral face. The lesson addresses Common Core standard 6.G.4 and applies these skills to real-life problems.

Section 1

Nets of Pyramids

Property

A net is a two-dimensional pattern that can be folded to form a three-dimensional shape.
For pyramids, the net shows the base and all triangular lateral faces laid flat in one plane.

Examples

Section 2

Surface Area Formulas for Square and Triangular Pyramids

Property

For a square pyramid: SA=s2+4⋅12⋅s⋅hlateralSA = s^2 + 4 \cdot \frac{1}{2} \cdot s \cdot h_{lateral}

For a triangular pyramid (equilateral base): SA=34⋅s2+3⋅12⋅s⋅hlateralSA = \frac{\sqrt{3}}{4} \cdot s^2 + 3 \cdot \frac{1}{2} \cdot s \cdot h_{lateral}

Section 3

Step-by-Step Surface Area Calculation Using Nets

Property

To find the surface area of a pyramid using nets:
(1) Draw or visualize the net showing all faces;
(2) Identify the base shape and calculate its area;
(3) Calculate the area of each triangular lateral face;
(4) Add all areas together using SA=Abase+Alateral1+Alateral2+...+AlateralnSA = A_{base} + A_{lateral1} + A_{lateral2} + ... + A_{lateraln}

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 8: Surface Area and Volume

  1. Lesson 1

    Lesson 1: Three-Dimensional Figures

    LearnPractice
  2. Lesson 2

    Lesson 2: Surface Areas of Prisms

    LearnPractice
  3. Lesson 3Current

    Lesson 3: Surface Areas of Pyramids

    LearnPractice
  4. Lesson 4

    Lesson 4: Volumes of Rectangular Prisms

    LearnPractice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Nets of Pyramids

Property

A net is a two-dimensional pattern that can be folded to form a three-dimensional shape.
For pyramids, the net shows the base and all triangular lateral faces laid flat in one plane.

Examples

Section 2

Surface Area Formulas for Square and Triangular Pyramids

Property

For a square pyramid: SA=s2+4⋅12⋅s⋅hlateralSA = s^2 + 4 \cdot \frac{1}{2} \cdot s \cdot h_{lateral}

For a triangular pyramid (equilateral base): SA=34⋅s2+3⋅12⋅s⋅hlateralSA = \frac{\sqrt{3}}{4} \cdot s^2 + 3 \cdot \frac{1}{2} \cdot s \cdot h_{lateral}

Section 3

Step-by-Step Surface Area Calculation Using Nets

Property

To find the surface area of a pyramid using nets:
(1) Draw or visualize the net showing all faces;
(2) Identify the base shape and calculate its area;
(3) Calculate the area of each triangular lateral face;
(4) Add all areas together using SA=Abase+Alateral1+Alateral2+...+AlateralnSA = A_{base} + A_{lateral1} + A_{lateral2} + ... + A_{lateraln}

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 8: Surface Area and Volume

  1. Lesson 1

    Lesson 1: Three-Dimensional Figures

    LearnPractice
  2. Lesson 2

    Lesson 2: Surface Areas of Prisms

    LearnPractice
  3. Lesson 3Current

    Lesson 3: Surface Areas of Pyramids

    LearnPractice
  4. Lesson 4

    Lesson 4: Volumes of Rectangular Prisms

    LearnPractice