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

Lesson 5.85.8 Small Group · Group 2

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, explain why the method works, and use it on a problem I have not seen before.

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. square base + 4 triangles
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. 4 on a square pyramid
BaseSpanish: Base The flat bottom of a pyramid. the square on the net
ApexSpanish: Ápice The point at the top of a pyramid where the sides meet. tip of the pyramid
Lateral areaSpanish: Área lateral The total area of just the side triangles, not the bottom. For a square pyramid: lateral area = 4 × (½ × base edge × slant height)

How it worksWorked examplesurface area of a square pyramid

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

A square pyramid has a base 10 cm on each side. Each triangular face has a slant height of 12 cm. Find the surface area.

  1. The net is a square base with 4 congruent triangles, one on each side.
  2. Area of the square base. 10 × 10 = 100
  3. One triangular face uses the slant height. ½ × 10 × 12 = 60
  4. Four faces plus the base. 60 × 4 = 240, then 240 + 100 = 340

Answer: The surface area is 340 square centimeters (340 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 14 in. on each side and a slant height of 9 in. Find the surface area.

  1. Sketch the net. Square: Triangles:
  2. Area of the square base. × = in²
  3. One triangular face. ½ × × = in²
  4. All the faces. × = , then + = in²
Answer:surface area of the pyramid

Say it and write itSentence starters

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

  • The base is a with an area of .
  • Each triangular face has a base of and a slant height of .
  • There are triangular faces, so together they cover .
  • The surface area is because I added .

Word bank pyramidbaseslant heightlateral faceapextrianglesquarecongruentaddsurface areasquare unitsnet

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 5.85.8 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

Part 1Understand the ideamodels and meaning
  1. 1Complete each step, then write the final answer.

    A camping tent is a square pyramid with a floor. The base is 7 ft by 7 ft. The slant height is 6 ft. Fabric costs $2 for each square foot. What does the fabric cost?

    Show your work
    Final answer:
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.
    6 ft16 ft10 ft slant
    A side view. The slant height runs along a face.

    A square pyramid has a base edge of 16 ft. Its height, from the floor to the top, is 6 ft. Its slant height is 10 ft. Find its surface area.

    1. 1Which height do the triangle faces use?
    2. 2What is the area of the base?
    3. 3What is the area of the four triangle faces?
    4. 4What is the surface area?
    Final answer:
  2. 3Complete each step, then write the final answer.
    base? cm8 cm

    A square pyramid has a base edge of 8 cm. Its surface area is 208 square centimeters. What is its slant height?

    1. 1Take away the base. How much area is on the 4 triangle faces?
    2. 2What is the area of one triangle face?
    3. 3Half of 8 × slant height is 36. What is the slant height?
    4. 4Why do we divide 144 by 4 before we use the triangle formula?
    Final answer:
  3. 4Complete 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:
  4. 5Complete each step, then write the final answer.

    A square pyramid has a slant height of 10 in. Its 4 triangle faces have a total area of 240 square inches. How long is each base edge?

    Show your work
    Final answer:
  5. 6Complete 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:

Explain your thinkingA pyramid has two heights. How do you decide which one to use for the faces? Use Lee's mistake to explain.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help