Math by First Principles
Level 2 · Intermediate ← Back to lesson

Areas of Regular Polygons: Practice

12 multiple-choice questions, progressively harder.

Level 2 · Intermediate 0 / 12 answered
Question 1 of 12
  1. 1

    A square has radius 727\sqrt2 cm. What is its area?

    The apothem and half-side are the legsAn enlarged schematic right triangle OMB. OM is perpendicular to MB at M. OM is labeled apothem a, MB is labeled half-side s/2, and OB is labeled radius 7√2 cm. The angle at O is labeled θ. Lengths and angle size must come from the text, not measurement.OMBapothemahalf-side s/2radius 7√2 cmθ
  2. 2

    An equilateral triangle has side length 16 cm. Which is its exact area?

    The apothem and half-side are the legsAn enlarged schematic right triangle OMB. OM is perpendicular to MB at M. OM is labeled apothem a, MB is labeled half-side s/2, and OB is labeled radius r. The angle at O is labeled θ. Lengths and angle size must come from the text, not measurement.OMBapothemahalf-side s/2radius rθ
  3. 3

    A regular pentagon has side length 10 cm. Which expression gives its apothem in centimeters? Use degrees.

    The apothem and half-side are the legsAn enlarged schematic right triangle OMB. OM is perpendicular to MB at M. OM is labeled apothem a, MB is labeled half-side s/2, and OB is labeled radius r. The angle at O is labeled θ. Lengths and angle size must come from the text, not measurement.OMBapothemahalf-side s/2radius rθ
  4. 4

    A convex regular decagon has radius 6 cm. Which is its apothem in centimeters? Use degrees.

    The apothem and half-side are the legsAn enlarged schematic right triangle OMB. OM is perpendicular to MB at M. OM is labeled apothem a, MB is labeled half-side s/2, and OB is labeled radius 6 cm. The angle at O is labeled θ. Lengths and angle size must come from the text, not measurement.OMBapothemahalf-side s/2radius 6 cmθ
  5. 5

    A regular hexagon has perimeter 78 cm and area 50732\tfrac{507\sqrt3}{2} square cm. What is its apothem?

  6. 6

    A regular hexagon has side length 323\sqrt2 cm. What is its exact area?

  7. 7

    A regular octagon has apothem 3 cm. Which expression gives its perimeter in centimeters? Use degrees.

    The apothem and half-side are the legsAn enlarged schematic right triangle OMB. OM is perpendicular to MB at M. OM is labeled apothem 3 cm, MB is labeled half-side s/2, and OB is labeled radius r. The angle at O is labeled θ. Lengths and angle size must come from the text, not measurement.OMBapothem3 cmhalf-side s/2radius rθ
  8. 8

    A regular dodecagon has radius 11 cm. Which calculation finds half a side in centimeters? Use degrees.

    The apothem and half-side are the legsAn enlarged schematic right triangle OMB. OM is perpendicular to MB at M. OM is labeled apothem a, MB is labeled half-side s/2, and OB is labeled radius 11 cm. The angle at O is labeled θ. Lengths and angle size must come from the text, not measurement.OMBapothemahalf-side s/2radius 11 cmθ
  9. 9

    A square has area 225 square cm. What is its apothem?

  10. 10

    An equilateral triangle has radius 10 cm and side length 10310\sqrt3 cm. What is its apothem?

    The apothem and half-side are the legsAn enlarged schematic right triangle OMB. OM is perpendicular to MB at M. OM is labeled apothem a, MB is labeled half-side s/2, and OB is labeled radius 10 cm. The angle at O is labeled θ. Lengths and angle size must come from the text, not measurement.OMBapothemahalf-side s/2radius 10 cmθ
  11. 11

    A convex regular polygon has central angle 72 degrees and radius 14 cm. Which is its apothem in centimeters?

    The apothem and half-side are the legsAn enlarged schematic right triangle OMB. OM is perpendicular to MB at M. OM is labeled apothem a, MB is labeled half-side s/2, and OB is labeled radius 14 cm. The angle at O is labeled θ. Lengths and angle size must come from the text, not measurement.OMBapothemahalf-side s/2radius 14 cmθ
  12. 12

    Which change turns the center-triangle area sum into half the perimeter times the apothem?

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