Math by First Principles
Level 1 · Foundational ← Back to lesson

Areas of Regular Polygons: Practice

12 multiple-choice questions, progressively harder.

Level 1 · Foundational 0 / 12 answered
Question 1 of 12
  1. 1

    In the schematic regular polygon, which segment is the apothem?

    Center triangles fill a regular polygonSchematic convex regular 6-gon with center O. Segments from O to the endpoints of the bottom side show center triangles. The bottom side is labeled side BC. A dashed perpendicular from O meets the midpoint M of that side, is segment OM, and has a right-angle mark. The radius to the right endpoint is segment OB. No computed answers are labeled.OMside BCBC
  2. 2

    What is one central angle of a convex regular nonagon?

  3. 3

    Joining the center of a convex regular pentagon to every vertex creates how many nonoverlapping center triangles?

    Center triangles fill a regular polygonSchematic convex regular 5-gon with center O. Segments from O to every vertex show center triangles. The bottom side is labeled s. A dashed perpendicular from O meets the midpoint M of that side, is labeled a, and has a right-angle mark. The radius to the right endpoint is labeled r. No computed answers are labeled.OMarsBC
  4. 4

    A convex regular hexagon has perimeter 72 cm and apothem 636\sqrt3 cm. What is its exact area?

    Center triangles fill a regular polygonSchematic convex regular 6-gon with center O. Segments from O to every vertex show center triangles. The bottom side is labeled side s. A dashed perpendicular from O meets the midpoint M of that side, is labeled a, and has a right-angle mark. The radius to the right endpoint is labeled r. No computed answers are labeled.OMarside sBC
  5. 5

    A square has side length 18 cm. What is its apothem?

    Center triangles fill a regular polygonSchematic convex regular 4-gon with center O. Segments from O to every vertex show center triangles. The bottom side is labeled side 18 cm. A dashed perpendicular from O meets the midpoint M of that side, is labeled a, and has a right-angle mark. The radius to the right endpoint is labeled r. No computed answers are labeled.OMarside 18 cmBC
  6. 6

    Which fact ensures that each segment from the interior center to a boundary point stays inside the polygon?

  7. 7

    For a convex regular hexagon, how does its radius compare with its side length?

    Center triangles fill a regular polygonSchematic convex regular 6-gon with center O. Segments from O to every vertex show center triangles. The bottom side is labeled s. A dashed perpendicular from O meets the midpoint M of that side, is labeled a, and has a right-angle mark. The radius to the right endpoint is labeled r. No computed answers are labeled.OMarsBC
  8. 8

    What is the half-central angle used in a right half-triangle of an equilateral triangle?

    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
  9. 9

    A square has perimeter 28 cm and apothem 3.5 cm. What is its area?

  10. 10

    A convex regular polygon has a central angle of 24 degrees. How many sides does it have?

  11. 11

    Which rule gives the area of a convex regular polygon with perimeter P and apothem a?

  12. 12

    In a convex regular polygon of positive side length, which statement compares radius r and apothem a?

    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
← Back to lesson