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Unit 08 · Area Volume and Surface AreaLesson

Day 108Parallelograms and Trapezoids

LearnClassworkAnswer keyPDF packet ↗
Standards 6.G.A.1
LEARNING TARGET

I can find parallelogram and trapezoid areas by rearranging shapes.

01 · LEARN

Build the idea

Cut and move a corner of a parallelogram to make a rectangle: A = bh. Two matching trapezoids form a parallelogram, giving A = (b1 + b2)h/2. Heights must be perpendicular.

WORKED EXAMPLE 1

A parallelogram has base 7 m and perpendicular height 6 m. Sketch how it can be rearranged into a rectangle and find its area.

42 m²

Cut and shift a corner; A = bh = 7 × 6 = 42.

WORKED EXAMPLE 2

A trapezoid has parallel bases 14 m and 20 m and perpendicular height 6 m. Sketch it and find its area.

102 m²

A = (14 + 20) × 6 ÷ 2 = 102.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. A parallelogram has base 3 m and perpendicular height 4 m. Sketch how it can be rearranged into a rectangle and find its area.

  2. A parallelogram has base 7 m and perpendicular height 5 m. Sketch how it can be rearranged into a rectangle and find its area.

  3. A parallelogram has base 2 m and perpendicular height 4 m. Sketch how it can be rearranged into a rectangle and find its area.

  4. A trapezoid has parallel bases 10 m and 22 m and perpendicular height 3 m. Sketch it and find its area.

  5. A trapezoid has parallel bases 10 m and 20 m and perpendicular height 7 m. Sketch it and find its area.

  6. A trapezoid has parallel bases 6 m and 18 m and perpendicular height 3 m. Sketch it and find its area.

  7. A trapezoid has parallel bases 12 m and 22 m and perpendicular height 5 m. Sketch it and find its area.

  8. A trapezoid has parallel bases 4 m and 10 m and perpendicular height 5 m. Sketch it and find its area.

  9. A trapezoid has parallel bases 16 m and 28 m and perpendicular height 6 m. Sketch it and find its area.

  10. A trapezoid has parallel bases 12 m and 24 m and perpendicular height 4 m. Sketch it and find its area.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 12 m²

    Cut and shift a corner; A = bh = 3 × 4 = 12.

  2. 35 m²

    Cut and shift a corner; A = bh = 7 × 5 = 35.

  3. 8 m²

    Cut and shift a corner; A = bh = 2 × 4 = 8.

  4. 48 m²

    A = (10 + 22) × 3 ÷ 2 = 48.

  5. 105 m²

    A = (10 + 20) × 7 ÷ 2 = 105.

  6. 36 m²

    A = (6 + 18) × 3 ÷ 2 = 36.

  7. 85 m²

    A = (12 + 22) × 5 ÷ 2 = 85.

  8. 35 m²

    A = (4 + 10) × 5 ÷ 2 = 35.

  9. 132 m²

    A = (16 + 28) × 6 ÷ 2 = 132.

  10. 72 m²

    A = (12 + 24) × 4 ÷ 2 = 72.

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