Math 2HonorsName ______
Lesson 8-3: Area of a Regular PolygonDate ______
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:
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 buildingis composed of two regular pentagons with the same center, called Ground Zero.
Just how big is the Pentagon?
Follow the process belowto find out.
Show your work to find the area of the Pentagon in ft2.
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?
OVER
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I.An interesting fact about the Pentagon: It is possible to get from the furthest points in under 10 minutes.
It requires taking a shortcut through the open courtyard and Ground Zero by walking very fast.
- Draw a line segment representing this path.
- Find the length of this path in feet.
- The distance from endzone to endzone of a football field is 300 feet. How many “football fields” make up this 10-minute walk?
- What 2 special segments of the Pentagon were connected to represent the path?
II.The area of the Pentagon that you previously calculated included the area of the open courtyard.
What is the area of just the building in square feet?
Use the following fact to help you in your computations:
The open courtyard’s acreage is 5 acres.
Show your work to find the area of just the building in ft2.
III. Notes:
- Describe how to find the measure of the vertex angle of one of the isosceles triangles in a regular polygon.
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Homework:
Show your work for the following problems. Label your answers with the appropriate units. Round to the nearest 100th.
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.Find the area of the regular polygon below.
24 mm
3.The area of a regular decagon is 1522 yd2 and the apothem is 22.25 yd. Find the length of each side.
4. Find the area of the equilateral triangle below.
16 in.
38 in.
5.The length of a side of a regular dodecagon is 52 inches. Find the length of the apothem.
6. The apothem of a regular pentagon is 25 ft. Find the length of the radius.
OVER
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7. A regular decagon has a perimeter of 88.46 yd. Find the lengths of the decagon’s apothem and radius.
8.Find the area of the regular hexagonal “donut”.
a = 6.928cm r = 8cm
9.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 nonagon.
10.Now that Ralph has finished turning 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 as 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.