Name:________________________Date:____________________________pd:____
Areas of Regular Polygons-Grade Worksheet
Directions: This is going to count as a quiz grade. Show all work to receive full credit. Circle
your final answer when appropriate. Include all formulas used to find your answer. Make sure
to answer all questions completely. Good Luck. 
Part 1: Multiple Choice
(1 point each)
Place the correct answer choice on the space provided.
_____1. The figure at the right is a regular octagon with radii and an apothem drawn. What is
the m1?
A. 22.5
B. 45
C. 60
D. 67.5
_____2.
A.
B.
C.
D.
What is m2 ?
22.5
45
60
67.5
_____3. A regular pentagon has an apothem of 3.2 m and an area of 37.2 m2. What is the
length of one side of the pentagon?
A. 3.96 m
B. 4.65 m
C. 11.875 m
D. 23.75 m
_____4.
A.
B.
C.
D.
What is the area of the square at the right?
16.97 cm2
72 cm2
144 cm2
288 cm2
_____5. A regular hexagon has a perimeter 60 in. What is the hexagon’s area?
A. 150 3 in 2
B. 75 3 in 2
C. 300 3 in 2
D. 600 3 in 2
_____6.
A.
B.
C.
D.
For which regular polygon can you not sue special right triangles to find the apothem?
Pentagon
Triangle
Square
Hexagon
_____7. What is the area of the regular pentagon at the right?
A. 688.2 ft2
B. 394.1 ft2
C. 229.1 ft2
D. 458.2 ft2
_____8.
A.
B.
C.
D.
What is the area of a regular hexagon with sides 8 cm?
110.1 cm2
166.3 cm2
309.0 cm2
332.6 cm2
_____9.
A.
B.
C.
D.
What is the area of a regular nonagon with a radius of 14 in?
70.9 in2
141.7 in2
566.9 in2
1211.6 in2
_____10. What is the area of the triangle to the right?
A. 6.0 ft2
B. 8.6 ft2
C. 15.0 ft2
D. 17.2 ft2
Part 2: Short Answer
(3 point each)
Show all work. List all formulas used to solve any problems.
11. The triangles below are similar. What is the ratio (larger to smaller) of the perimeters?
12. What is the ratio of the areas for the triangles from #11?
13. The pentagons below are similar. The area of the smaller pentagon is 30 square meters.
What is the area of the larger pentagon?
14. It costs $350 to carpet a 8 ft by 10 ft room. At this rate, how many dollars would it cost
to put the same carpeting in a 24 ft by 30 ft room?
15. The area of two similar octagons are 112 square inches and 63 square inches. What is the
ratio (smaller to larger) of their perimeters?
Part 3: Short Answer (4 point each) Show all work. List all formulas used to solve any problems.
Leave your answers in simplest radical form.
16. Find the area of the shaded region below. All shapes in the figures are regular polygons.
18. Find the area of the shaded region below. All shapes in the figures are regular polygons.
19. The area of an equilateral triangle is 108 3 ft 2 . What is the length of a side and the
apothem ? Draw a diagram.