Area of a regular polygon

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

1. 1.

   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?

   • OF
   • CF
   • CD
   • OC
2. 2.

   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?

   • OC
   • OF
   • CD
   • CF
3. 3.

   Kira's regular hexagon floor tile is made of 6 equilateral triangles with 10 cm sides. OF goes from center O to F, the midpoint of side CD. How long is OF, as a simplified radical?

   5√3
4. 4.

   Luz's regular hexagon quilt patch is made of 6 equilateral triangles with 16 cm sides. OF goes from center O to F, the midpoint of side CD. How long is OF, as a simplified radical?

   8√3
5. 5.

   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?

   10√3
6. 6.

   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?

   110

7. Read this first

   Use this

   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).

8. 7.

   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?

   1086
9. 8.

   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?

   276

10. Use this

    Sketch, not to scale: the hexagon with all 6 triangles drawn from O. Triangle OCD is shaded: base CD = 4 inches, height OF = 3.5 inches (the apothem), slanted side OC = 4 inches (the radius).

11. 9.

    Zee cuts a regular hexagon tile into 6 equal triangles from its center O. Each has base 4 inches and height 3.5 inches. What is the tile's area, in square inches?

    42
12. 10.

    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?

    99