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Grade 10 · Math · Geometry

10th grade Area of a regular polygon worksheet

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Area of a regular polygon

Grade 10 Math Worksheet - Challenge Me

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Circle the best answer, or write your answer on the line.

  1. A regular hexagon name badge in Bo's craft box has an apothem of 3 cm. What is its area in square centimeters, as a simplified radical?

  2. A regular hexagon plate in Esme's craft box has an apothem of 9 cm. What is its area in square centimeters, as a simplified radical?

  3. A regular hexagon mirror in Jun's craft box has an apothem of 15 cm. What is its area in square centimeters, as a simplified radical?

  4. Read this first

    Use this

    Sketch, not to scale: square with center O. OC = 3√2 inches runs to corner C; OF meets side CD at its midpoint F at a right angle.

  5. Kira's square sticky note has center O. Its radius, from O to corner C, is 3√2 inches. What is the area of the sticky note, in square inches?

  6. Use this

    Sketch, not to scale: square with center O. OC = 7√2 inches runs to corner C; OF meets side CD at its midpoint F at a right angle.

  7. Luz's square window has center O. Its radius, from O to corner C, is 7√2 inches. What is the area of the window, in square inches?

  8. Use this

    Sketch, not to scale: square with center O. OC = 15√2 inches runs to corner C; OF meets side CD at its midpoint F at a right angle.

  9. Milo's square table top has center O. Its radius, from O to corner C, is 15√2 inches. What is the area of the table top, in square inches?

  10. Noah's pond deck is a regular pentagon with 5 sides. Its area is 1450 ft² and its apothem is 20 feet. How long is each side, in feet?

  11. Pia's rug is a regular nonagon with 9 sides. Its area is 1584 in² and its apothem is 22 inches. How long is each side, in inches?

  12. Ren's plate is a regular heptagon with 7 sides. Its area is 2646 cm² and its apothem is 28 cm. How long is each side, in centimeters?

  13. Ari's garden bed is an equilateral triangle with 18-foot sides. Its apothem runs from center O to F, the midpoint of side CD. What is its area in square feet, as a simplified radical?

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10th grade Area of a regular polygon worksheet – printable
Print: 123456

About this worksheet

Area of a regular polygon. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find the apothem of a regular polygon and tell it apart from the radius.
  • I can find the area of a regular polygon as ½ × apothem × perimeter.
  • I can use a 30-60-90 or 45-45-90 triangle to find an exact apothem.

Standard: G-MG.A.1

Words to know

regular polygon: All sides equal and all angles equal.

center: The point the same distance from every corner.

apothem: From the center to the middle of a side, meeting it square.

radius (of a polygon): From the center to a corner.

perimeter: The distance around: all the sides added.

simplified radical: A root with no square left inside, like 4√3.

Common mistakes

Multiplied the apothem by the perimeter but left out the ½. Each triangle around the center is half of a rectangle. Cut a paper square along its diagonal together to see the half.

Found the area of one triangle but not of the whole shape. The shape is made of several equal triangles.

Used the radius (center to a corner) as the height instead of the apothem (center to the middle of a side).

What to say

Ask: how many triangles meet at the center?

Ask: which segment meets the side at a right angle?

Questions parents ask

What is the most common mistake with area of a regular polygon?

Multiplied the apothem by the perimeter but left out the ½. Each triangle around the center is half of a rectangle. Cut a paper square along its diagonal together to see the half.

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More geometry

See all Geometry

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