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 - Building Confidence

NameDate

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

1.
Ari's clock face is a regular octagon with center O. C and D are corners next to each other, and F is the midpoint of CD. Which segment is the apothem?
- OC
- CD
- CF
- OF
2.
Bo's stepping stone is a regular pentagon with center O. C and D are corners next to each other, and F is the midpoint of CD. Which segment is the apothem?
- OF
- CD
- OC
- CF
3.
Esme's paper badge is a regular decagon with center O. C and D are corners next to each other, and F is the midpoint of CD. Which segment is the apothem?
- OC
- CD
- CF
- OF
4.
Jun's window is a regular dodecagon with center O. C and D are corners next to each other, and F is the midpoint of CD. Which segment is the apothem?
- CD
- CF
- OC
- OF
Milo's regular hexagon mirror is made of 6 equilateral triangles with 26 cm sides. OF goes from center O to F, the midpoint of side CD. How long is OF, as a simplified radical?
Noah's regular hexagon stepping stone is made of 6 equilateral triangles with 20 cm sides. OF goes from center O to F, the midpoint of side CD. How long is OF, as a simplified radical?
Pia cuts a regular pentagon paper sticker into 5 equal triangles from its center O. Each has base 8 cm and height 5.5 cm. What is the paper sticker's area, in square centimeters?
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Sketch, not to scale: the octagon with all 8 triangles drawn from O. Triangle OCD is shaded: base CD = 15 inches, height OF = 18.1 inches (the apothem), slanted side OC = 19.6 inches (the radius).
Ren cuts a regular octagon table top into 8 equal triangles from its center O. Each has base 15 inches and height 18.1 inches. What is the table top's area, in square inches?
Tala cuts a regular decagon plate into 10 equal triangles from its center O. Each has base 6 cm and height 9.2 cm. What is the plate's area, in square centimeters?
Ari cuts a regular nonagon name badge into 9 equal triangles from its center O. Each has base 4 cm and height 5.5 cm. What is the name badge's area, in square centimeters?

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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