Area of a regular polygon

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 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?

   18√3

2. 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.

3. 2.

   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?

   36

4. 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.

5. 3.

   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?

   196

6. 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.

7. 4.

   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?

   900
8. 5.

   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?

   29
9. 6.

   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?

   16
10. 7.

    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?

    27
12. 8.

    Tala's road sign is an equilateral triangle with 30-inch sides. Its apothem runs from center O to F, the midpoint of side CD. What is its area in square inches, as a simplified radical?

    225√3
13. 9.

    Zee's window is an equilateral triangle with 24-inch sides. Its apothem runs from center O to F, the midpoint of side CD. What is its area in square inches, as a simplified radical?

    Use the picture in question 8.

    144√3
14. 10.

    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?

    Use the picture in question 8.

    81√3