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

Lesson 5.85.7 · 5.8 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 5.7 · 5.8 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

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

WordWhat it meansExample
Surface Area of PrismsSpanish: Área de superficie de prismas The total area of all bases and lateral faces of a prism. Formula: SA = 2B + lateral area. SA = 2B + lateral area
Surface areaSpanish: Área de superficie The total area of all the flat sides of a solid. Paint every outside surface of a box — the total painted area is the surface area
Rectangular prismSpanish: Prisma rectangular A solid box shape with six flat rectangle sides. A box with 6 flat rectangle sides: top, bottom, front, back, left, right
Triangular prismSpanish: Prisma triangular A solid with two triangle ends and three flat rectangle sides. Shaped like a tent or a wedge of cheese — 2 triangle ends + 3 rectangle sides
FaceSpanish: Cara One flat side of a solid shape. A triangular prism has 5 faces: 2 triangles + 3 rectangles
NetSpanish: Plantilla (desarrollo plano) A flat shape that folds up into a solid. Unfold a triangular prism flat: you see 2 triangles and 3 rectangles side by side

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 5.85.7 · 5.8 Catch-Up

Catch-UpSkill bridge

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can show I am caught up on Lessons 5.7 · 5.8 by using each lesson's big idea in mixed practice.

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

    (Lesson 5.7) What is the surface area of a rectangular prism with l = 5 cm, w = 4 cm, h = 3 cm?

    1. A47 cm²
    2. B60 cm²
    3. C94 cm²
    4. D94 cm³

    Hint You need surface area — the total of all 6 face areas of the 5 × 4 × 3 prism — not the space inside.

    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. 2Circle the letter of the best answer. Show how you know.

    (Lesson 5.7) How many faces does a triangular prism have?

    1. A3
    2. B4
    3. C5
    4. D6

    Hint Picture a tent or a triangular chocolate box: two triangle ends plus rectangles wrapping around the sides.

    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    (Lesson 5.8) A square pyramid has a base edge of 5 in and a slant height of 7 in. What is the surface area?

    1. A70 in²
    2. B95 in²
    3. C95 in³
    4. D120 in²

    Hint A square pyramid has TWO kinds of faces: one square base (5 × 5) and four identical triangles with slant height 7.

    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. 4Circle the letter of the best answer. Show how you know.

    (Lesson 5.8) How many lateral (triangular) faces does a square pyramid have?

    1. A3
    2. B4
    3. C5
    4. D6

    Hint Lateral faces are the slanted triangles on the sides — the square base itself doesn't count.

    Show your work

Explain your thinkingDisplay B has the largest surface area (280 in²). What contributes more to the total — the base or the lateral faces? Why?

Sentence starter For Display B, the base area is ___ in² and the total lateral area is 4 × ___ = ___ in². The ___ contribute(s) more because ___.

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