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Unit 08 · Area Volume and Surface AreaLesson

Day 107Triangle Heights and Fractional Measures

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

I can find the area of any triangle using a perpendicular height.

01 · LEARN

Build the idea

Two matching triangles form a parallelogram, so A = (base × perpendicular height)/2. A slanted side is not necessarily the height. Label area in square units.

WORKED EXAMPLE 1

Sketch a triangle with base 12 cm and perpendicular height 3 cm. Find its area.

18 cm²

A = bh/2 = 12 × 3 ÷ 2 = 18. Two such triangles make a parallelogram.

WORKED EXAMPLE 2

Sketch a triangle with base 6 cm and perpendicular height 7/2 cm. Find its area. Explain why the slanted side is not needed.

21/2 cm²

A = bh/2 = 6 × 7/2 ÷ 2 = 21/2. Two such triangles make a parallelogram.

02 · PRACTICE

Your turn

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

  1. Sketch a triangle with base 4 cm and perpendicular height 7 cm. Find its area.

  2. Sketch a triangle with base 4 cm and perpendicular height 3 cm. Find its area.

  3. Sketch a triangle with base 16 cm and perpendicular height 7 cm. Find its area.

  4. Sketch a triangle with base 4 cm and perpendicular height 6 cm. Find its area.

  5. Sketch a triangle with base 10 cm and perpendicular height 7 cm. Find its area.

  6. Sketch a triangle with base 4 cm and perpendicular height 4 cm. Find its area.

  7. Sketch a triangle with base 8 cm and perpendicular height 2 cm. Find its area. Explain why the slanted side is not needed.

  8. Sketch a triangle with base 14 cm and perpendicular height 5/2 cm. Find its area. Explain why the slanted side is not needed.

  9. Sketch a triangle with base 10 cm and perpendicular height 2 cm. Find its area. Explain why the slanted side is not needed.

  10. Sketch a triangle with base 8 cm and perpendicular height 1 cm. Find its area. Explain why the slanted side is not needed.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 14 cm²

    A = bh/2 = 4 × 7 ÷ 2 = 14. Two such triangles make a parallelogram.

  2. 6 cm²

    A = bh/2 = 4 × 3 ÷ 2 = 6. Two such triangles make a parallelogram.

  3. 56 cm²

    A = bh/2 = 16 × 7 ÷ 2 = 56. Two such triangles make a parallelogram.

  4. 12 cm²

    A = bh/2 = 4 × 6 ÷ 2 = 12. Two such triangles make a parallelogram.

  5. 35 cm²

    A = bh/2 = 10 × 7 ÷ 2 = 35. Two such triangles make a parallelogram.

  6. 8 cm²

    A = bh/2 = 4 × 4 ÷ 2 = 8. Two such triangles make a parallelogram.

  7. 8 cm²

    A = bh/2 = 8 × 2 ÷ 2 = 8. Two such triangles make a parallelogram.

  8. 35/2 cm²

    A = bh/2 = 14 × 5/2 ÷ 2 = 35/2. Two such triangles make a parallelogram.

  9. 10 cm²

    A = bh/2 = 10 × 2 ÷ 2 = 10. Two such triangles make a parallelogram.

  10. 4 cm²

    A = bh/2 = 8 × 1 ÷ 2 = 4. Two such triangles make a parallelogram.

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