Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.GR.3

Lesson 7.7Designing Polygons with a Scale

Apply Day · Set BSecond form · new problems, same idea

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Learning target I can draw polygons from their vertex coordinates on the coordinate plane, and use coordinates to find side lengths and solve perimeter and area problems.

Remember7.7 · Part II

Polygons on the Coordinate Plane

  1. Plot all given vertices and connect them in order to form the polygon
  2. Find side lengths by counting grid units or using coordinate distance formulas
  3. Perimeter = Sum of all side lengths; Area = Use standard polygon formulas

Words: vertex (vértice)polygon (polígono)perimeter (perímetro)distance between vertices (distancia entre vértices)scale (escala)

  1. 1Complete each step, then write the final answer.

    A rectangle has vertices (1, 2), (7, 2), (7, 5) and (1, 5). Find its perimeter.

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    A rectangle has vertices (−1.5, 3), (4, 3), (4, −2) and (−1.5, −2). Find its perimeter.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    The top side of a rectangle goes from (−3, 4) to (5, 4). The area is 48 square units. What is the y-coordinate of the bottom side?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    A soccer field on a map has corners (−50, 30), (50, 30), (50, −30) and (−50, −30). Each unit is 1 yard. How many yards is it around the field?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A school draws its playground on a grid. The corners are (−20, 10), (25, 10), (25, −10) and (−20, −10). Each unit is 1 meter. How many meters of fence go all the way around?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.
    −5−4−3−2−1123456−3−2−11234(−4, 3)(2, 3)(2, 0)(5, 0)(5, −2)(−4, −2)
    An L-shape. Split it into two rectangles.

    A polygon has vertices (−4, 3), (2, 3), (2, 0), (5, 0), (5, −2) and (−4, −2). Find its area.

    Show your work
    Final answer:
  7. 7Circle the letter of the best answer. Show how you know.

    Vertices (-4.5, 3) and (5, 3) share y = 3. What is the distance between them?

    1. A0.5 units
    2. B1.5 units
    3. C8 units
    4. D9.5 units
    My work — one step per lineWhat I did to both sides
  8. 8Circle the letter of the best answer. Show how you know.

    Vertices (5, 3) and (5, -3.75) share x = 5. What is the distance between them?

    1. A0.75 units
    2. B5 units
    3. C6.75 units
    4. D8.75 units
    My work — one step per lineWhat I did to both sides
  9. 9Circle the letter of the best answer. Show how you know.

    What is the perimeter of the rectangle with side lengths 9.5 and 6.75 units?

    1. A16.25 units
    2. B26 units
    3. C32.5 units
    4. D64.125 units
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
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