Math 2Name ______

Lesson 6-3: Area of a Regular Polygon

Learning Goals:

  • I can explain how to use the dissection method on regular polygons to generate an area formula for regular polygons: .
  • I can set up and solve equations involving the formula of a regular polygon:

I. Notes

For the equilateral triangle below, please do the following:

  1. Add the radii to to divide the triangle into 3 congruent isosceles triangles.
  2. Draw one apothem.
  3. Write the area of one isosceles triangle in terms of a (apothem length) and s (side length).
  4. Write the area of the triangle in terms of a and s.
  5. Record your results in the table.
  6. Repeat the process for the square and hexagon.
  7. Complete the rest of the table.

Number of sides / 3 / 4 / 5 / 6 / 7 / 8 / … / n
Area of the Regular Polygon / …

Area of a Regular Polygon: ______OVER 

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.

The buildingis composed of two regular pentagons (inside and outside) with the same center, called Ground Zero.

If the length of one of its outside sides is 921 feet,

find the area Pentagon.

Hints:You will need trig to find the apothem!

The sum of the angles in any regular

polygon is , n = # of sides

The radii of a regular polygon bisect

each angle

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?

Math 2Name ______

Lesson 6-3: Area of a Regular PolygonHomework

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.

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 apothem of a regular pentagon is 25 ft. Find the length of the radius.

5.Find the area of the regular hexagonal “donut”.

a = 6.928cm r = 8cm

6.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 approximately19 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.