Math by First Principles
Level 3 · Challenge ← Back to lesson

Areas of Regular Polygons: Practice

12 multiple-choice questions, progressively harder.

Level 3 · Challenge 0 / 12 answered
Question 1 of 12
  1. 1

    A square and a regular hexagon each have perimeter 24 cm. Which has greater area, and by how much?

    Compare the stated common measurementSeparate schematic panels show a square and a regular hexagon, each labeled perimeter 24 cm. The square outline is solid blue and the hexagon outline dashed red. No computed side length, apothem, or area is supplied.squareregular hexagonperimeter 24 cmperimeter 24 cm
  2. 2

    Which complete list of exact dimensions can belong to a square? All lengths use centimeters.

  3. 3

    A regular octagon has radius 12 cm. What is its area to the nearest tenth of a square centimeter? 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 12 cm. The angle at O is labeled θ. Lengths and angle size must come from the text, not measurement.OMBapothemahalf-side s/2radius 12 cmθ
  4. 4

    The half-central angle of a convex regular polygon is 7.5 degrees. How many sides does the polygon have?

  5. 5

    A square and a regular hexagon both have apothem 2 cm. What is the hexagon-to-square area ratio?

    Compare the stated common measurementSeparate schematic panels show a square and a regular hexagon, each with a perpendicular apothem labeled 2 cm. Right-angle marks show the feet. The square outline is solid blue and the hexagon outline dashed red. No side length or computed area is supplied.squareregular hexagon2 cm2 cm
  6. 6

    For a regular pentagon with positive side length x, which expression gives its area? Use degrees.

  7. 7

    A convex regular polygon has side length exactly twice its apothem. How many sides does it have?

    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
  8. 8

    An equilateral triangle has radius 18 cm. What 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 18 cm. The angle at O is labeled θ. Lengths and angle size must come from the text, not measurement.OMBapothemahalf-side s/2radius 18 cmθ
  9. 9

    A regular hexagon has apothem 15 cm. Which is its radius?

    The apothem and half-side are the legsAn enlarged schematic right triangle OMB. OM is perpendicular to MB at M. OM is labeled apothem 15 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.OMBapothem15 cmhalf-side s/2radius rθ
  10. 10

    Can a convex regular polygon have a half-central angle of exactly 27 degrees?

  11. 11

    A regular decagon has apothem 7 cm. What is its area to the nearest tenth? 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 7 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.OMBapothem7 cmhalf-side s/2radius rθ
  12. 12

    A convex regular polygon has central angle 20 degrees and apothem 4 cm. Which expression gives its area in square 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 4 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.OMBapothem4 cmhalf-side s/2radius rθ
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