Perimeter of Compound Shapes · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Perimeter of Compound Shapes

Mathematics · Measurement · ages 9-10
Name ______________________   Date ____________

  1. An L-shaped tile has six sides: 5 cm, 2 cm, 3 cm, 4 cm, 2 cm, and 6 cm. Mia added them up and got 20 cm. Is Mia correct?

    Circle one:   True   False

  2. An L-shaped room has six straight walls. Going around the room, the wall lengths are 10 cm, 3 cm, 4 cm, 3 cm, 6 cm, and 6 cm. What is the perimeter of the room?

    Answer: ______________

  3. To find the perimeter of a compound shape, what should you do?

    • Add up every outside side
    • Multiply the length by the width
    • Count only the longest side

  4. In a compound shape, you only need to add the longest sides to find the perimeter.

    Circle one:   True   False

  5. A garden bed is shaped like a 9 m by 6 m rectangle with a rectangular corner missing, making a step shape. The missing corner piece is 4 m wide and 2 m tall. What is the perimeter of the garden bed?

    • 26 m
    • 30 m
    • 34 m
    • 36 m

  6. A compound shape has a left side of 15 cm. Its lower right step is 9 cm tall. What is the height of the missing upper step?

    • 4 cm
    • 6 cm
    • 9 cm

  7. A field is a rectangle 12 m long and 7 m wide, but a smaller rectangle has been cut out of one corner. The missing piece is 5 m wide and 3 m tall. Two of the field's six side lengths are not given. What is the perimeter of the field?

    Answer: ______________

  8. A composite rectilinear shape has five known sides: 9 cm, 4 cm, 5 cm, 3 cm, and 9 cm. What must the sixth side measure so the perimeter is exactly 40 cm?

    • 8 cm
    • 9 cm
    • 10 cm
    • 12 cm

  9. A room is a 15 cm by 9 cm rectangle with a 6 cm by 4 cm rectangular corner missing. What is the perimeter of the room?

    • 42 cm
    • 44 cm
    • 46 cm
    • 48 cm

  10. Ben measured an L-shaped patio and listed six sides: 9 m, 4 m, 5 m, 4 m, 4 m, 8 m. He added them up and got 30 m by mistake. What is the correct perimeter?

    • 30 m
    • 32 m
    • 34 m
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Answer key

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

Perimeter of Compound Shapes W1-mt_n0AlyLQwC9-s1

  1. False · Adding all six sides gives 5+2+3+4+2+6 = 22 cm, not 20 cm, so Mia must have missed a side.
  2. 32 · Adding all six wall lengths gives 10+3+4+3+6+6 = 32 cm.
  3. Add up every outside side · Perimeter is the distance all the way around, so every outside side gets added, even the short step sides.
  4. False · Every side counts, not just the long ones. Skipping short sides gives the wrong total.
  5. 30 m · The hidden sides are 6-2=4 m and 9-4=5 m. Adding all six sides (9+4+4+2+5+6) gives 30 m.
  6. 6 cm · The two step heights must add up to match the left side: 15 - 9 = 6 cm.
  7. 38 · The hidden sides are 7-3=4 m and 12-5=7 m. Adding all six sides (12+4+5+3+7+7) gives 38 m.
  8. 10 cm · The five known sides add up to 30 cm, so the missing side is 40-30 = 10 cm.
  9. 48 cm · The hidden sides are 15-6=9 cm and 9-4=5 cm. Adding all six sides (9+9+15+5+6+4) gives 48 cm.
  10. 34 m · Adding all six sides carefully: 9 + 4 + 5 + 4 + 4 + 8 = 34 m. It's easy to drop a side by accident.
Worksheet · LightMySky