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

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Bo's flower bed in the park is a regular pentagon with 5 sides of 20 feet. Its apothem is 13.8 feet and its radius is 17 feet. What is its area, in square feet?
Esme's window is a regular octagon with 8 sides of 25 cm. Its apothem is 30.2 cm and its radius is 32.7 cm. What is its area, in square centimeters?
Jun's park stage floor is a regular decagon with 10 sides of 13 feet. Its apothem is 20 feet and its radius is 21 feet. What is its area, in square feet?
Luz's mirror is a regular heptagon with 7 sides of 10 inches. Its apothem is 10.4 inches and its radius is 11.5 inches. What is its area, in square inches?
Milo's rug is a regular nonagon with 9 sides of 12 inches. Its apothem is 16.5 inches and its radius is 17.5 inches. What is its area, in square inches?
Noah makes a regular hexagon sticker with sides of 4 cm. What is the area of the sticker in square centimeters, as a simplified radical?
Pia makes a regular hexagon name badge with sides of 6 cm. What is the area of the name badge in square centimeters, as a simplified radical?
Ren makes a regular hexagon tile with sides of 8 cm. What is the area of the tile in square centimeters, as a simplified radical?
Tala makes a regular hexagon quilt patch with sides of 12 cm. What is the area of the quilt patch in square centimeters, as a simplified radical?
Zee makes a regular hexagon clock face with sides of 14 cm. What is the area of the clock face in square centimeters, as a simplified radical?

10th grade Area of a regular polygon worksheet – printable — Print: 1 2 3 4 5 6

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.

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