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Unit 08 · Area Volume and Surface AreaLesson

Day 111Polygons on the Coordinate Plane

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

I can draw polygons from coordinates and use side lengths to find area.

01 · LEARN

Build the idea

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.

WORKED EXAMPLE 1

Plot and connect (0,0), (8,0), (8,10), (0,10). Find the side lengths and area.

Sides 8 and 10; area 80 square units

Horizontal length 8 - (0) = 8; vertical length 10 - (0) = 10; area = 8 × 10.

WORKED EXAMPLE 2

Plot and connect (-5,-4), (4,-4), (4,4), (-5,4). Find the side lengths and area. Find the perimeter too.

Sides 9 and 8; area 72 square units; perimeter 34 units

Horizontal length 4 - (-5) = 9; vertical length 4 - (-4) = 8; area = 9 × 8.

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), (10,12), (0,12). Find the side lengths and area.

  2. Plot and connect (0,0), (11,0), (11,8), (0,8). Find the side lengths and area.

  3. Plot and connect (0,0), (6,0), (6,10), (0,10). Find the side lengths and area.

  4. Plot and connect (-2,-4), (2,-4), (2,2), (-2,2). Find the side lengths and area.

  5. Plot and connect (-3,-7), (2,-7), (2,2), (-3,2). Find the side lengths and area.

  6. Plot and connect (-8,-2), (3,-2), (3,3), (-8,3). Find the side lengths and area.

  7. Plot and connect (-5,-7), (5,-7), (5,5), (-5,5). Find the side lengths and area. Find the perimeter too.

  8. Plot and connect (-5,-4), (6,-4), (6,6), (-5,6). Find the side lengths and area. Find the perimeter too.

  9. Plot and connect (-8,-5), (2,-5), (2,2), (-8,2). Find the side lengths and area. Find the perimeter too.

  10. Plot and connect (-3,-2), (2,-2), (2,2), (-3,2). Find the side lengths and area. Find the perimeter too.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. Sides 10 and 12; area 120 square units

    Horizontal length 10 - (0) = 10; vertical length 12 - (0) = 12; area = 10 × 12.

  2. Sides 11 and 8; area 88 square units

    Horizontal length 11 - (0) = 11; vertical length 8 - (0) = 8; area = 11 × 8.

  3. Sides 6 and 10; area 60 square units

    Horizontal length 6 - (0) = 6; vertical length 10 - (0) = 10; area = 6 × 10.

  4. Sides 4 and 6; area 24 square units

    Horizontal length 2 - (-2) = 4; vertical length 2 - (-4) = 6; area = 4 × 6.

  5. Sides 5 and 9; area 45 square units

    Horizontal length 2 - (-3) = 5; vertical length 2 - (-7) = 9; area = 5 × 9.

  6. Sides 11 and 5; area 55 square units

    Horizontal length 3 - (-8) = 11; vertical length 3 - (-2) = 5; area = 11 × 5.

  7. Sides 10 and 12; area 120 square units; perimeter 44 units

    Horizontal length 5 - (-5) = 10; vertical length 5 - (-7) = 12; area = 10 × 12.

  8. Sides 11 and 10; area 110 square units; perimeter 42 units

    Horizontal length 6 - (-5) = 11; vertical length 6 - (-4) = 10; area = 11 × 10.

  9. Sides 10 and 7; area 70 square units; perimeter 34 units

    Horizontal length 2 - (-8) = 10; vertical length 2 - (-5) = 7; area = 10 × 7.

  10. Sides 5 and 4; area 20 square units; perimeter 18 units

    Horizontal length 2 - (-3) = 5; vertical length 2 - (-2) = 4; area = 5 × 4.

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