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Unit 10 · Final Applications and ReviewLesson

Day 136Designing a School Garden

LearnClassworkAnswer keyPDF packet ↗
Standards 6.G.A.36.G.A.1
LEARNING TARGET

I can use coordinates and polygon areas to plan a garden.

01 · LEARN

Build the idea

Read the requested quantity first and identify the relevant model. Plot vertices in order and connect them, including the last to the first. Equal x-values make a vertical side; equal y-values make a horizontal side. Count or subtract coordinates to get the side lengths. Explain why the units and the final value fit the situation.

WORKED EXAMPLE 1

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

12 cm²

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

WORKED EXAMPLE 2

A trapezoid has parallel bases 12 m and 22 m and perpendicular height 4 m. Sketch it and find its area.

68 m²

A = (12 + 22) × 4 ÷ 2 = 68.

02 · PRACTICE

Your turn

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

  1. Plot and connect (0,0), (10,0), (10,9), (0,9). Find the side lengths and area.

  2. Sketch a triangle with base 12 cm and perpendicular height 2 cm. Find its area.

  3. An L-shaped garden is a 12 m by 9 m rectangle with an 8 m by 5 m corner rectangle removed. Sketch and find the garden area.

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

  5. Plot and connect (-2,-3), (5,-3), (5,5), (-2,5). Find the side lengths and area.

  6. Sketch a triangle with base 6 cm and perpendicular height 7 cm. Find its area.

  7. A 10 m by 9 m rectangle has a right-triangle corner removed with perpendicular legs 6 m and 3 m. Sketch the remaining polygon and find its area.

  8. A trapezoid has parallel bases 10 m and 16 m and perpendicular height 2 m. Sketch it and find its area.

  9. Plot and connect (-7,-6), (3,-6), (3,3), (-7,3). Find the side lengths and area. Find the perimeter too.

  10. Sketch a triangle with base 14 cm and perpendicular height 7/2 cm. Find its area. Explain why the slanted side is not needed.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. Sides 10 and 9; area 90 square units

    Horizontal length 10 - (0) = 10; vertical length 9 - (0) = 9; area = 10 × 9.

  2. 12 cm²

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

  3. 68 m²

    Outer area 108 minus cutout 40 = 68.

  4. 64 m²

    A = (10 + 22) × 4 ÷ 2 = 64.

  5. Sides 7 and 8; area 56 square units

    Horizontal length 5 - (-2) = 7; vertical length 5 - (-3) = 8; area = 7 × 8.

  6. 21 cm²

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

  7. 81 m²

    Whole rectangle 90; remove triangle 9; difference 81.

  8. 26 m²

    A = (10 + 16) × 2 ÷ 2 = 26.

  9. Sides 10 and 9; area 90 square units; perimeter 38 units

    Horizontal length 3 - (-7) = 10; vertical length 3 - (-6) = 9; area = 10 × 9.

  10. 49/2 cm²

    A = bh/2 = 14 × 7/2 ÷ 2 = 49/2. Two such triangles make a parallelogram.

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