Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.2Determine the Area of Triangles

Set B · Version ASecond form · supported practice

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

Learning target I can find the area of a triangle using the formula A = ½ × base × height.

Why This Matters Your architecture firm is designing a park with triangular garden beds. The client wants to know exactly how much soil to order, which means calculating the area of each triangular section. The first garden has a base of 12 feet and a height of 8 feet.

RememberDetermine the Area of Triangles

Area of Triangles. Formula: Area = ½ × Base × Height (A = ½ b · h) A triangle has three sides. The base is one side, and the height is the straight-up (perpendicular) distance from the base to the top corner.

  1. Identify the base and the perpendicular height to that base.
  2. A triangle is exactly half of a rectangle with the same base and height.
  3. Multiply base by height, then divide by 2

Words: Base (Base)Height (Altura)Area (Área)Perpendicular (Perpendicular)Composite figure (Figura compuesta)

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

    What is the area of a rectangle 8 cm long and 5 cm wide?

    1. A13 square cm
    2. B26 square cm
    3. C40 square cm
    4. D40 cubic cm
    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.

    What is the area of a parallelogram with base 9 in and height 4 in?

    1. A13 square in
    2. B18 square in
    3. C26 square in
    4. D36 square in
    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?
  3. 3Circle the letter of the best answer. Show how you know.

    In a parallelogram, how is the height measured?

    1. AAlong the slanted side
    2. BPerpendicular to the base
    3. CAround the outside
    4. DFrom one corner to the opposite corner
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    A parallelogram has an area of 48 square cm and a base of 8 cm. What is its height?

    1. A6 cm
    2. B40 cm
    3. C56 cm
    4. D384 cm
    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?
  5. 5Circle the letter of the best answer. Show how you know.

    A homeowner wants to paint one triangular wall of an A-frame cabin. The wall has a base of 20 feet and a height of 14 feet. One can of paint covers 50 square feet. What is the area of the triangular wall?

    1. A34 sq ft
    2. B70 sq ft
    3. C140 sq ft
    4. D280 sq ft
    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?
  6. 6Circle the letter of the best answer. Show how you know.

    A homeowner wants to paint one triangular wall of an A-frame cabin. The wall has a base of 20 feet and a height of 14 feet. One can of paint covers 50 square feet. How many cans of paint does she need?

    1. A2
    2. B2.8
    3. C3
    4. D4
    Show your work

Explain your thinkingThe triangle fits inside a 12 × 8 rectangle. How does the triangle's area compare to the rectangle's area?

Sentence starter The area of the triangle is ___ the rectangle because A = 1/2 × ___ × ___ = ___ square feet.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
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.1

Lesson 5.2Determine the Area of Triangles

Set B · Version BSecond form · core practice

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

Learning target I can find the area of a triangle using the formula A = ½ × base × height.

Why This Matters Your architecture firm is designing a park with triangular garden beds. The client wants to know exactly how much soil to order, which means calculating the area of each triangular section. The first garden has a base of 12 feet and a height of 8 feet.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each triangular plan on the blueprint to its area. Use A = ½ × base × height.

    1. Triangle base 10, height 6
    2. Triangle base 7, height 4
    3. Triangle base 9, height 8
    4. Triangle base 16, height 3
    5. Triangle base 5, height 8
    6. Triangle base 11, height 2
    • A30 sq ft
    • B14 sq ft
    • C36 sq ft
    • D24 sq ft
    • E20 sq ft
    • F11 sq ft
  2. 2Write the name of the correct group on each line.

    An intern at the firm gave two answers for each triangular wall. Sort each answer into the CORRECT area (½ × base × height) or the FORGOT THE HALF mistake (just base × height).

    Groups: Correct area (½ × base × height) Forgot the ½ (just base × height)
    • Wall base 18, height 6 → 54 sq ft
    • Wall base 18, height 6 → 108 sq ft
    • Wall base 20, height 5 → 50 sq ft
    • Wall base 20, height 5 → 100 sq ft
    • Wall base 14, height 8 → 56 sq ft
    • Wall base 14, height 8 → 112 sq ft
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A homeowner wants to paint one triangular wall of an A-frame cabin. The wall has a base of 20 feet and a height of 14 feet. One can of paint covers 50 square feet. Why round up instead of down?

    1. ABecause 2 cans cover only 100 sq ft, which is not enough for 140
    2. BBecause paint is always sold in threes
    3. CBecause 2.8 rounds to 3 by the usual rule
    4. DBecause the wall might be bigger
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    A triangular window in the firm's lobby has a base of 10 ft and a height of 6 ft. What is its area?

    1. A16 sq ft
    2. B30 sq ft
    3. C32 sq ft
    4. D60 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  3. 5Circle the letter of the best answer. Show how you know.

    A triangular roof panel on the blueprint has a base of 7 ft and a height of 4 ft. What is its area?

    1. A11 sq ft
    2. B14 sq ft
    3. C22 sq ft
    4. D28 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  4. 6Circle the letter of the best answer. Show how you know.

    On the blueprint, a triangular garden bed has a base of 11 ft and a height of 6 ft. What is its area?

    1. A17 sq ft
    2. B30 sq ft
    3. C33 sq ft
    4. D66 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit

Explain your thinkingThe triangle fits inside a 12 × 8 rectangle. How does the triangle's area compare to the rectangle's area?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help