Scale and similar shapes · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Scale and similar shapes

Mathematics · Ratio & Proportion · ages 10-11
Name ______________________   Date ____________

  1. A photo is 4 inches wide. Jeff enlarges it using a scale factor of 3 to make a poster. How wide, in inches, is the poster?

    Answer: ______________

  2. Rectangle A has a width of 5 cm. Rectangle B is similar to Rectangle A, with a scale factor of 3. What is the width of Rectangle B, in cm?

    Answer: ______________

  3. A small rectangle has a side of 4 cm. It is enlarged with a scale factor of 3. What is the matching side on the big rectangle?

    Small side4
    • 7 cm
    • 12 cm
    • 8 cm

  4. A small triangle has a side of 6 cm. The matching side on a similar big triangle is 18 cm. What is the scale factor?

    Smalltriangleside6Bigtriangleside18
    • 3
    • 12
    • 24

  5. A rectangle 3 cm by 7 cm is enlarged with a scale factor of 4. Which of these is the new rectangle's size?

    • 12 cm by 28 cm
    • 7 cm by 3 cm
    • 6 cm by 14 cm
    • 12 cm by 21 cm

  6. Two similar triangles have matching sides of 5 cm and 20 cm. What is the scale factor from the smaller triangle to the larger one?

    Answer: ______________

  7. Triangle A has a side of 6 cm. The matching side on similar Triangle B is 18 cm. What is the scale factor from Triangle A to Triangle B?

    • 2
    • 3
    • 4
    • 6

  8. A shape has sides 2 cm, 3 cm and 5 cm. It is enlarged with a scale factor of 3. Which set of sides is correct for the new shape?

    • 6 cm, 9 cm, 15 cm
    • 5 cm, 6 cm, 8 cm
    • 6 cm, 9 cm, 8 cm

  9. Reya scales a rectangle with sides 4 cm and 7 cm by a factor of 3. She writes the new sides as 12 cm and 10 cm. What mistake did she make?

    • She used the wrong scale factor for both sides
    • She swapped the two side lengths
    • She multiplied one side but added to the other

  10. A model bridge is similar to the real bridge, with a scale factor of 3 from model to real. The model's support beam is 2.5 cm long. How long, in cm, is the real support beam?

    Answer: ______________

LightMySky · lightmysky.comW1-mt_2OtRUM_0zW-s1

Answer key

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

Scale and similar shapes W1-mt_2OtRUM_0zW-s1

  1. 12 · Enlarging by a scale factor means multiplying every length by that factor.
  2. 15 · Multiplying a side by the scale factor gives you the matching side on the new shape.
  3. 12 cm · Multiply the small side by the scale factor: 4 x 3 = 12 cm.
  4. 3 · Divide the big side by the small side: 18 / 6 = 3.
  5. 12 cm by 28 cm · Every side of the rectangle gets multiplied by the same scale factor.
  6. 4 · Dividing the larger matching side by the smaller one gives the scale factor.
  7. 3 · The scale factor is the new side divided by the matching old side.
  8. 6 cm, 9 cm, 15 cm · Multiply every side by 3: 2x3=6, 3x3=9, 5x3=15. All three sides must use the same scale factor.
  9. She multiplied one side but added to the other · 4 x 3 = 12 is correct, but 7 x 3 should be 21. She got 10 by adding 3 to 7 instead of multiplying.
  10. 7.5 · Multiplying the model's length by the scale factor gives the real length.
Worksheet · LightMySky