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

Lesson 5.2Determine the Area of Triangles

Start hereWords, worked example, and sentence starters

Name Date Period

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

Start hereWords for this lesson

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

WordWhat it meansExample
BaseSpanish: Base Any side of a triangle can be the base. Once you pick a base, the height must be measured perpendicular (at a 90° angle) to it. b in A = ½bh
HeightSpanish: Altura The straight-up distance from the base to the top corner. h in A = ½bh
AreaSpanish: Área How much space is inside a flat shape. measured in cm², in², ft²
PerpendicularSpanish: Perpendicular Two lines that meet to make a square corner (90 degrees). The corner of a book or a door frame — the edges meet at exactly 90°, shown by a small square symbol
Composite figureSpanish: Figura compuesta A shape made by putting two or more simple shapes together. A house shape = a rectangle (the walls) + a triangle (the roof); total area = rectangle area + triangle area
FormulaSpanish: Fórmula A math rule written with symbols. A = ½ × b × h means Area equals one-half times base times height; for b = 12 and h = 8, A = 48

How it worksWorked examplefinding the area of a triangle

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

A triangle has a base of 16 cm and a perpendicular height of 9 cm. Find the area.

  1. Two copies of a triangle form a parallelogram, so a triangle is half of one.
  2. Write the formula. A = ½ × b × h
  3. Name the parts. b = 16 cm h = 9 cm, meeting the base at a square corner
  4. Multiply, then halve. 16 × 9 = 144, and half of 144 is 72

Answer: The area of the triangle is 72 square centimeters (72 cm²).

Now you trySame steps, your turn

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

A triangle has a base of 14 in. and a perpendicular height of 7 in. Find the area.

  1. A triangle is half of what shape?
  2. Write the formula. A = ½ × ×
  3. Base = in. Perpendicular height = in.
  4. Multiply, then halve. × = , half is
Answer:area of the triangle

Say it and write itSentence starters

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

  • The base of the triangle is and the height is .
  • I know that measure is the height because .
  • Two copies of this triangle would compose a .
  • Area = ½ × × = square units.

Word bank triangleparallelogramhalfbaseheightperpendicularsquare cornerareaformularight trianglecopyrotate

Watch outA common mistake

A common mistake in Area of Triangles is forgetting the ½ — students multiply base × height like a rectangle and stop there, or they use the triangle's slanted side instead of the perpendicular height that's already given. Always check: did I take half, and did I use the straight-up height, not the slanted side?

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

Lesson 5.2Determine the Area of Triangles

Version ASupported 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.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Use the formula A = ½ × b × h to find the area of each triangle.

    TriangleBaseHeightArea
    Sail A6 ft8 ft
    Sail B10 ft5 ft

    Hint Each sail row gives one base and one height — the blank Area column is yours to fill.

    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    What is the area of a triangle with base 10 cm and height 6 cm?

    1. A16 sq cm
    2. B30 sq cm
    3. C30 cm
    4. D60 sq cm

    Hint You have a base of 10 cm and a height of 6 cm — a triangle needs only those two, plus one special step.

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

    A triangle has an area of 24 sq ft and a base of 8 ft. What is the height?

    1. A3 ft
    2. B6 ft
    3. C12 ft
    4. D16 ft

    Hint The area (24 sq ft) and base (8 ft) are given — you're solving backwards for the height.

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

    Why do we divide by 2 when finding the area of a triangle?

    1. AA triangle is exactly half of a rectangle with the same base and height
    2. BTriangles have 2 equal sides
    3. CThe base is always twice the height
    4. DWe always divide area formulas by 2

    Hint Think about drawing a diagonal across a rectangle — what two shapes does it create?

    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    What is the area of a triangle with base 14 ft and height 6 ft?

    1. A20 sq ft
    2. B42 sq ft
    3. C42 ft
    4. D84 sq ft

    Hint Base 14 ft and height 6 ft — remember what makes a triangle's area different from a rectangle's.

    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?
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Identify base and heightbase = 9 ft, height = 4 ft
    2. 2Write the formulaA = ½ × base × height
    3. 3Multiply base × height9 × 4 = 36
    4. 4Final answerA = 36 sq ft

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Look at the formula: A = ½ × base × height. Does the final answer include the ½?

    Correct work
    Correct answer:

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.

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

Version BCore 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.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Complete the table.

    TriangleBaseHeightArea
    Garden A12 ft8 ft
    Garden B9 ft27 sq ft
    Garden C10 ft35 sq ft
    Garden D15 ft4 ft
    Show your work
  2. 2Write the letter of the matching item on each line.

    Match each shape to its area. Watch the rule: triangles use A = ½ × base × height, but parallelograms and rectangles use A = base × height (do NOT take half).

    1. Triangle b=8, h=6
    2. Triangle b=10, h=8
    3. Triangle b=12, h=5
    4. Parallelogram b=5, h=4
    5. Rectangle 7×3
    6. Parallelogram b=9, h=2
    • A24 sq units
    • B40 sq units
    • C30 sq units
    • D20 sq units
    • E21 sq units
    • F18 sq units
  3. 3Write the name of the correct group on each line.

    Calculate the area of each triangle. Sort by whether the area is greater than 30 sq units or not.

    Groups: Area > 30 sq units Area ≤ 30 sq units
    • b=10, h=8
    • b=6, h=9
    • b=14, h=5
    • b=8, h=7
    • b=12, h=6
    • b=10, h=6
  4. 4Mark and label each value on the number line.

    Find the missing height: b = 10, A = 35

    0123456789101112
    Show your thinking
Part 2Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Identify base and heightbase = 12 ft, height = 7 ft
    2. 2Write the formulaA = ½ × base × height
    3. 3Substitute valuesA = ½ × 12 × 7
    4. 4CalculateA = (½ × 12) × (½ × 7) = 6 × 3.5 = 21 sq ft

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

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

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

ChallengeExtension

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.

Part 1Understand the ideamodels and meaning
  1. 1Use the model to solve. Show your work.
    Total8080

    Rectangle 16×10 = 160 sq ft split into two equal triangles of 80 sq ft each

    Show your work
    Answer:
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Area Error

    1. 1Identify base and heightb = 14 m, h = 9 m
    2. 2Write the formulaA = ½ × b × h
    3. 3Substitute valuesA = ½ × 14 × 9
    4. 4CalculateA = ½ × 23 = 11.5 sq m

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A rectangle is 12 ft by 8 ft. A diagonal line cuts it into two triangles. What is the area of each triangle? Explain how the triangle area formula relates to the rectangle area formula.

    Write your answer

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

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