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.

   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?

   • CD
   • OF
   • CF
   • OC
2. 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
   • CF
   • OC
   • CD
3. 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?

   • CF
   • OC
   • OF
   • CD
4. 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?

   • OC
   • OF
   • CF
   • CD
5. 5.

   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
6. 6.

   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?

   13√3
7. 7.

   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

8. 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).

9. 8.

   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

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