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

Lesson 5.8Lateral Area of Pyramids

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the surface area of a pyramid by adding the base area and the lateral faces.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
PyramidSpanish: Pirámide A solid with a flat bottom and triangle sides that meet at one point on top. base + slanted faces
Slant heightSpanish: Altura inclinada (apotema) The height of a side triangle, measured along its slanted face. used in ½ × b × slant
Lateral faceSpanish: Cara lateral A triangle side of a pyramid, not the bottom. the slanted sides
BaseSpanish: Base The flat bottom of a pyramid. A square pyramid sits on a square base; base area = side × side
ApexSpanish: Ápice The point at the top of a pyramid where the sides meet. The pointy top of a pyramid — all the slanted edges connect here
Lateral areaSpanish: Área lateral The total area of just the side triangles, not the bottom. base is left out

How it worksWorked examplecovering only the slanted faces

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A pyramid has a triangle base with sides of 18 cm. Each of its 3 slanted faces has a slant height of 20 cm. Find the area of the slanted faces only.

  1. The net is one triangle base with 3 slanted triangles around it.
  2. Only the slanted faces get covered, so leave the base out of the total.
  3. One slanted face. ½ × 18 × 20 = 180
  4. All three slanted faces. 180 × 3 = 540

Answer: The slanted faces cover 540 square centimeters (540 cm²).

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A square pyramid has a base 11 in. on each side and a slant height of 16 in. Find the area of the slanted faces only.

  1. Sketch the net. Base shape: Slanted faces:
  2. Does the base belong in this total? Why?
  3. One slanted face. ½ × × =
  4. All the slanted faces. × = in²
Answer:area of the slanted faces

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • This pyramid has slanted faces.
  • Each slanted face has an area of square units.
  • I the base because .
  • The total area I need is square units.

Word bank pyramidbaseslant heightlateral facelateral areasurface areaincludeleave outaddtrianglesquarenet

Watch outA common mistake

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?'

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

Lesson 5.8Lateral Area of Pyramids

Apply Day · Version ASupported 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.

  1. 1Complete each step, then write the final answer.
    base5 in2 in

    A square pyramid has a base that is 2 in by 2 in. Its slant height is 5 in. Find its surface area.

    Show your work

    Hint Find the base. Then find the 4 triangle faces. Add them.

    Final answer:
  2. 2Complete each step, then write the final answer.

    A square pyramid has a base that is 6 cm by 6 cm. Its slant height is 4 cm. Find its surface area.

    Show your work

    Hint One triangle face is half of 6 × 4.

    Final answer:
  3. 3Complete each step, then write the final answer.

    A square pyramid has a base that is 4 m by 4 m. Its slant height is 3 m. Find its surface area.

    Show your work

    Hint Base: 4 × 4. One face: half of 4 × 3. Then add the base and 4 faces.

    Final answer:
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 5.8Lateral Area of Pyramids

Apply Day · Version BCore 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.

  1. 1Complete each step, then write the final answer.

    A square pyramid has a base edge of 8 in and a slant height of 6 in. Ty writes 4 × (8 × 6) + 64 = 256. What is the correct surface area?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    A square pyramid has a base edge of 2.5 m. Its slant height is 4 m. Find its surface area.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    A square pyramid has a base that is 12 cm by 12 cm. Its slant height is 10 cm. Find its surface area.

    Show your work
    Final answer:
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 5.8Lateral Area of Pyramids

Apply Day · ChallengeExtension

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.

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

    A square pyramid has a base measuring 6 m by 6 m and four triangular faces, each with a base of 6 m and a slant height of 5 m. What is its surface area?

    1. A36 square meters
    2. B60 square meters
    3. C96 square meters
    4. D156 square meters
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  2. 2Complete each step, then write the final answer.

    A square pyramid has a base edge of 18 cm, a height of 12 cm and a slant height of 15 cm. Lee uses 12 cm for the triangle faces and gets 756. Find the correct surface area.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    A square pyramid has a base edge of 14 in. Its height is 24 in. Its slant height is 25 in. Find its surface area.

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help