Geometry-Area of Regular Polygons
Name___________________
Date_____________
1
Area of a Regular Polygon is A  aP
2
1. What does the a in the area formula for a regular polygon represent? How is this distance
measured?

2. How do you find the perimeter of a regular polygon?
3. What does it mean for a shape to be regular?
4. In the blank next to each figure, write how many sides each figure has.
a. Triangle _____
b. Hexagon _____
c. Octagon _____
d. Pentagon _____
e. Nonagon _____
f. Quadrilateral _____
g. Heptagon _____
h. Decagon _____
5. Find the area of a regular decagon with a 12.3-in. apothem and 8-in. sides.
6. Find the area of a regular pentagon with 11.6-cm sides and an 8-cm apothem.
7. Find the area of a regular heptagon with a 29.1-ft apothem and 28-ft sides.
8. The Smith family has decided to build an octagonal gazebo in their backyard. Each side is 8
ft long, and its apothem is 9.7 ft. What is the area enclosed by the gazebo?
Geometry-Area of Regular Polygons
Name___________________
Date_____________
9. A regular hexagon has a perimeter of 120 m and an apothem length of 23 m. Find the area.
10. The area of a regular octagonal garden is 1235.2 yd2. The apothem is 19.3 yd. What is the
perimeter of the garden?
11. The apothem of a stop sign is 24.1 inches and the length of each side is 20 inches. Find the
area of the stop sign.
12. The area of a regular nonagon is 378 square yards and the apothem is 10.5 yards. Find the
length of each side.
13. A quilt is made by sewing together interlocking regular hexagons. Each hexagon has an
apothem of 1.7 inches and a perimeter of 12 inches. About how many regular hexagons will it
take to make a quilt that is 6 feet by 8 feet?
14. The Pentagon in Washington D.C. has side lengths of 921 ft. The length of its apothem is
approximately 634 ft. What is the area of the pentagon?