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

Lesson 5.3Determine the Area of Trapezoids

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h.

Why This Matters Your architecture firm is designing a trapezoidal window for a modern building. The glass supplier charges by the square foot, so the team must calculate the exact area. The window has a top edge of 4 feet, a bottom edge of 8 feet, and a height of 5 feet.

Start hereWords for this lesson

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

WordWhat it meansExample
TrapezoidSpanish: Trapecio A four-sided shape with just one pair of parallel sides. top base and bottom base
ParallelSpanish: Paralelas Two lines or sides that stay the same distance apart and never meet. the two bases
Base 1 (b1)Spanish: Base 1 (b1) One of the two parallel sides of a trapezoid. If the bottom of the trapezoid is 10 ft, then b₁ = 10 ft in the formula A = ½(b₁ + b₂) × h
Base 2 (b2)Spanish: Base 2 (b2) The other parallel side of a trapezoid. If the top of the trapezoid is 6 ft, then b₂ = 6 ft; both bases are parallel to each other
HeightSpanish: Altura The straight-up distance between the two parallel sides. h, meets bases squarely
PerpendicularSpanish: Perpendicular Two lines that meet to make a square corner (90 degrees). The dashed height meets the base at a square corner — the small 90° box is what makes it perpendicular, not slanted.

How it worksWorked example

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

Bases 6 cm and 14 cm, height 5 cm, two matching triangles.

  1. Rectangle: 6 × 5 = 30 cm².
  2. Each triangle base: (14 − 6) ÷ 2 = 4 cm.
  3. Triangles: 2 × (½ × 4 × 5) = 20 cm².

Answer: 30 + 20 = 50 cm²

Now you trySame steps, your turn

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

Now a smaller trapezoid: bases 3 cm and 5 cm, height 2 cm.

Answer:

Say it and write itSentence starters

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

  • The two parallel bases are and .
  • I decomposed the trapezoid into and .
  • The pieces have areas , , and .
  • The total area is square units because .

Word bank trapezoidparallelbaseheightdecomposerectangletriangleleftoveraddtotalareasquare units

Watch out!A common mistake

A common mistake in Area of Trapezoids is forgetting the ½ in A = ½ × (b1 + b2) × h. After adding the bases and multiplying by the height, students stop there instead of taking half

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

Lesson 5.3Determine the Area of Trapezoids

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

Learning target I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h.

Why This Matters Your architecture firm is designing a trapezoidal window for a modern building. The glass supplier charges by the square foot, so the team must calculate the exact area. The window has a top edge of 4 feet, a bottom edge of 8 feet, and a height of 5 feet.

How it worksWorked example

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

Bases 6 cm and 14 cm, height 5 cm, two matching triangles.

  1. Rectangle: 6 × 5 = 30 cm².
  2. Each triangle base: (14 − 6) ÷ 2 = 4 cm.
  3. Triangles: 2 × (½ × 4 × 5) = 20 cm².

Answer: 30 + 20 = 50 cm²

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

    What is the area of a trapezoid with bases 6 cm and 10 cm, and height 4 cm?

    1. A24 sq cm
    2. B32 sq cm
    3. C40 sq cm
    4. D64 sq cm
    Steps to try
    1. A trapezoid has two bases (6 cm and 10 cm) plus a height (4 cm) — all three belong in the formula.
    2. Use A = ½ × (b₁ + b₂) × h: add the bases first, then multiply by the height, then take half.
    3. Add 6 + 10 to get the base sum, multiply that by 4, then cut the result in half.
    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.

    A trapezoid has an area of 45 sq ft, bases of 7 ft and 11 ft. What is the height?

    1. A3 ft
    2. B5 ft
    3. C9 ft
    4. D10 ft
    Steps to try
    1. You already know the area (45 sq ft) and both bases (7 ft and 11 ft) — the height is what's missing.
    2. Simplify first: ½ × (7 + 11) = 9. So the equation becomes 45 = 9 × h.
    3. Divide 45 by 9 to find the height in feet.
    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.

    What is the first step when finding the area of a trapezoid?

    1. AMultiply the two bases
    2. BSubtract the shorter base from the longer base
    3. CAdd the two bases together
    4. DDivide the height by 2
    Steps to try
    1. Look at the trapezoid formula A = ½ × (b₁ + b₂) × h. Parentheses show what happens first.
    2. Ask what (b₁ + b₂) means: are the two parallel bases combined by adding, multiplying, or subtracting?
    3. Say the formula in words: 'half of (base one ___ base two) times height.' The word that fills the blank is your first step.
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    A trapezoid has bases of 5 in and 9 in, and a height of 6 in. What is its area?

    1. A27 sq in
    2. B30 sq in
    3. C42 sq in
    4. D84 sq in
    Steps to try
    1. Circle the two bases (5 in and 9 in) and the height (6 in) — the trapezoid formula uses all three.
    2. Follow A = ½ × (b₁ + b₂) × h in order. Skipping the ½ makes your answer come out doubled.
    3. Compute 5 + 9 = 14 first, then multiply 14 × 6, and finally take half of that product.
    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?

Explain your thinkingIf you copied this trapezoid, flipped it, and placed it next to the original, what shape would you get? How does this help you find the area?

Sentence starter The area of the trapezoid is 1/2 x (___ + ___) x ___ = 1/2 x ___ x ___ = ___ 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