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

Lesson 5.3Determine the Area of Trapezoids

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 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.

RememberDetermine the Area of Trapezoids

Area of Trapezoids. Formula: Area = ½ × (b1 + b2) × h A trapezoid is a four-sided shape with one pair of parallel sides. The two parallel sides are called the bases, and they have different lengths.

  1. A trapezoid is a four-sided shape with one pair of parallel bases.
  2. Add the two bases together: (b1 + b2).
  3. Multiply by the perpendicular height, then take half

Words: Trapezoid (Trapecio)Parallel (Paralelas)Base 1 (b1) (Base 1 (b1))Base 2 (b2) (Base 2 (b2))Height (Altura)

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

    What is the area of a triangle with base 7 m and height 4 m?

    1. A11 square m
    2. B14 square m
    3. C14 m
    4. D28 square m
    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 triangle with base 12 cm and height 5 cm?

    1. A17 square cm
    2. B30 square cm
    3. C30 cm
    4. D60 square 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?
  3. 3Circle the letter of the best answer. Show how you know.

    A triangle has an area of 36 square inches and a base of 9 inches. What is its height?

    1. A4 inches
    2. B8 inches
    3. C27 inches
    4. D324 inches
    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.

    Why does the triangle area formula use ½?

    1. ATriangles always have half as many sides
    2. BThe height is always half the base
    3. CArea formulas always use ½
    4. DA triangle is half of a parallelogram with the same base and height
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A builder is pouring concrete for a trapezoidal driveway. The driveway has parallel edges of 20 feet and 12 feet with a height of 15 feet. One bag of concrete covers 6 square feet. What is the area of the trapezoidal driveway?

    1. A47 sq ft
    2. B120 sq ft
    3. C240 sq ft
    4. D480 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 builder is pouring concrete for a trapezoidal driveway. The driveway has parallel edges of 20 feet and 12 feet with a height of 15 feet. One bag of concrete covers 6 square feet. How many bags of concrete does the builder need?

    1. A6
    2. B24
    3. C40
    4. D240
    Show your work

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

Lesson 5.3Determine the Area of Trapezoids

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 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.

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Each blueprint window lists its bases and height. Find each area, then sort the windows by whether they need more than 40 sq ft of glass.

    Groups: More than 40 sq ft of glass 40 sq ft of glass or less
    • Window: b1=8, b2=6, h=5
    • Window: b1=10, b2=8, h=6
    • Window: b1=4, b2=2, h=9
    • Window: b1=11, b2=9, h=5
    • Window: b1=7, b2=3, h=6
    • Window: b1=13, b2=7, h=8
  2. 2Write the letter of the matching item on each line.

    Match each blueprint window to the area of glass it needs.

    1. Trapezoid window b1=6, b2=4, h=3
    2. Trapezoid window b1=9, b2=5, h=4
    3. Trapezoid window b1=10, b2=6, h=5
    4. Trapezoid window b1=12, b2=8, h=6
    • A15 sq ft
    • B28 sq ft
    • C40 sq ft
    • D60 sq ft
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A builder is pouring concrete for a trapezoidal driveway. The driveway has parallel edges of 20 feet and 12 feet with a height of 15 feet. One bag of concrete covers 6 square feet. Why add the two parallel edges and then take half?

    1. ABecause trapezoids are half of rectangles
    2. BBecause the average of the two bases acts like one rectangle's width
    3. CBecause 20 + 12 = 32 is easier
    4. DBecause the height must be halved
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    Blueprint 1: A trapezoidal lobby window has bases of 6 ft and 10 ft and a height of 4 ft. What is its area for the glass order?

    1. A16 sq ft
    2. B32 sq ft
    3. C40 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.

    Blueprint 2: A trapezoidal skylight has bases of 9 ft and 7 ft and a height of 6 ft. What is its area?

    1. A44 sq ft
    2. B48 sq ft
    3. C63 sq ft
    4. D96 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.

    Two equal trapezoid windows join to form a parallelogram with area 96 sq ft. What is the area of ONE trapezoid?

    1. A16 sq ft
    2. B48 sq ft
    3. C96 sq ft
    4. D192 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit

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?

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