Accurate drawing and scale diagrams · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Building shapes and reading scale drawings

Mathematics · Geometry · ages 11-13
Name ______________________   Date ____________

  1. Mia draws a small rectangle that is 3 cm long and 2 cm wide. She makes a scale drawing of it using a scale factor of 4. How long is the rectangle in her new drawing?

    • 7 cm
    • 12 cm
    • 8 cm
    • 6 cm

  2. Zoe draws a triangle with a 6 cm side, a 4 cm side, and a 30 degree angle between them. She has drawn the 6 cm side. Where does she place her protractor to mark the angle?

    • At one end of the 6 cm side, where the 4 cm side will begin
    • At the exact middle of the 6 cm side
    • At the corner opposite the 6 cm side

  3. On a scale drawing, if 1 cm stands for 5 m, a line measuring 3 cm on the drawing represents 15 m in real life.

    Circle one:   True   False

  4. You read a protractor and the pointer sits between the 47 and 48 degree marks, closer to 47. What do you record?

    • 47°
    • 48°
    • 47.5°

  5. A figure has two angles that look almost equal on paper. Your protractor readings are 62° and 65°. What should you trust?

    • The protractor readings, since angles that look similar can still differ
    • Your eyes, since the figure looks symmetric
    • Neither, guess an average of both angles

  6. Sam wants to draw a triangle with one side 5 cm long, another side 7 cm long, and a 40 degree angle between those two sides. Which two tools does Sam need to draw it accurately?

    • A compass and a calculator
    • A ruler and a protractor
    • Two rulers only
    • A protractor and string

  7. A big rectangle is 20 cm long and 12 cm wide. It is an exact scaled copy of a small rectangle that is 5 cm long and 3 cm wide. How many times bigger is the big rectangle than the small one?

    Answer: ______________

  8. A floor plan has a scale of 1 cm = 2 m. A bedroom wall measures 3.5 cm on the plan. How many meters long is the real wall?

    Answer: ______________

  9. Ravi read a scale drawing labeled '1 cm to 4 m'. He measured a garden path as 6 cm and calculated the real length as 6 + 4 = 10 m. What went wrong?

    • He added instead of multiplying the measurement by the scale
    • He used the wrong ruler
    • He measured the path in the wrong units

  10. To construct a triangle using SAS, given a 7 cm side, a 4 cm side, and a 38 degree included angle, how many separate measurements in total (side lengths plus the angle) must you mark with your ruler and protractor?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Building shapes and reading scale drawings W1-mt_Jf8xcX4UTq-s1

  1. 12 cm · A scale factor of 4 means every length is multiplied by 4, so 3 cm becomes 12 cm.
  2. At one end of the 6 cm side, where the 4 cm side will begin · The 30 degree angle is the included angle, so it must sit between the two given sides. It gets built at an end of the 6 cm side, where the 4 cm side will start.
  3. True · Multiply the ruler length by the scale: 3 times 5 equals 15 m.
  4. 47° · Round to the nearest whole degree mark, not to a half degree.
  5. The protractor readings, since angles that look similar can still differ · A protractor gives an exact reading in degrees. Appearances can be misleading, especially on small drawings.
  6. A ruler and a protractor · The ruler draws the exact side lengths and the protractor draws the exact 40 degree angle.
  7. 4 · Divide a matching pair of sides: 20 / 5 = 4, so the scale factor is 4.
  8. 7 · Multiply the plan length by the scale: 3.5 times 2 equals 7 m.
  9. He added instead of multiplying the measurement by the scale · Scale problems need multiplication, not addition. The real length is 6 times 4, or 24 m.
  10. 3 · SAS needs exactly three measurements: the two given side lengths and the one included angle between them.
Worksheet · LightMySky