Math 2
Lesson 6-4: Area of a Regular Polygon
Name ________________________________
Date ____________________________
Learning Goals:

I can explain how to use the dissection method on regular polygons to generate an area formula for regular
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polygons: 𝐴 = 2 ∙ 𝑎𝑝𝑜𝑡ℎ𝑒𝑚 ∙ 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟.
 I can set up and solve equations involving the formula of a regular polygon:
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𝐴 = ∙ 𝑎𝑝𝑜𝑡ℎ𝑒𝑚 ∙ 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟.
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I. Notes
Vocabulary Associated with Regular Polygons:
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Center C
Radius r
Central Angle
Side s
Apothem a
For the equilateral triangle below, please do the following:
1.
2.
3.
4.
5.
6.
7.
Add the radii to to divide the triangle into 3 congruent isosceles triangles.
Draw one apothem.
Write the area of one isosceles triangle in terms of a (apothem length) and s (side length).
Write the area of the triangle in terms of a and s.
Record your results in the table.
Repeat the process for the square and hexagon.
Complete the rest of the table.
Number of sides
Area of the
Regular Polygon
3
4
5
6
7
8
…
n
…
Area of a Regular Polygon: _________________________________________________
OVER 
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II. Examples:
1. If the distance from the center to a side of a stop sign is 91.61 cm and the length of each side is 75.9 cm,
find the area of the stop sign.
2. The area of a regular decagon is 1522 square yd2 and the apothem is 22.25 yd. Find the length of each
side.
3. On January 15, 1943, work was completed on the new headquarters for the U.S. War Department (the
modern-day Department of Defense) in Arlington, Virginia. The massive complex, commonly known as
the Pentagon, was built to house the nearly 30,000 defense workers tasked with helping America win
World War II. With more than 17 miles of corridors, it remains one of the largest office buildings in the
world.
 It is difficult to understand just how big the Pentagon is. In fact, the U.S. Capitol building could fit
into just one of the Pentagon’s five sides.
 The building is composed of two regular pentagons with the same center, called Ground Zero.
If the length of one of its sides is 921 feet,
find the area Pentagon.
Now convert the area of the Pentagon into acres. There are 43,560 square feet in one acre.
The acreage of Progressive Field is 12 acres. How many times larger is the Pentagon than Progressive
Field?
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III. Homework:
Show your work for the following problems. Label your answers with the appropriate units. Round to the
nearest 100th if you have to round.
1. Find the area of the regular polygon below.
18 mm
24 mm
2. The area of a regular hexagon is 125.8 cm2. If the apothem is 12 cm, what is the length of one side?
3. Find the area of the equilateral triangle below.
16 in.
38 in.
4. The length of a side of a regular dodecagon is 52 inches. Find the length of the apothem.
5. The apothem of a regular pentagon is 25 ft. Find the length of the radius.
6. A regular decagon has a perimeter of 88.46 yd. Find the lengths of the decagon’s apothem and radius.
OVER 
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7. Find the area of the regular hexagonal “donut”.
a = 6.928 cm
r = 8 cm
8. If the area of a regular nonagon is 1390.5 m2 and the length of each side is 15 m, find the length of a
radius of the decagon.
9. Find the area of a regular heptagon whose side length is 5 ft.
10. Now that Ralph has finished transforming his man cave into a home theater, he is turning his attention to
the deck off the back of his house. The deck needs to be re-sealed. The shape of the deck is a regular
octagon with a perimeter of 128 feet. The distance from the center of the deck to any side is
approximately 19 feet. Ralph knows that one gallon of sealant covers 125 square feet. After taking back
some Monster Cable that he did not need for his home theater, Ralph has an extra $225 with which to
buy the sealer (pictured below). Determine if this is enough money for Ralph to buy the amount of
sealer necessary to cover the deck with one coat.
Important!