Area and Perimeter of Regular Polygons
Name_______________________
1. A garden shaped like a regular hexagon has 3
walkways that divide the garden into 6 triangles.
All the triangles formed by the walkway are congruent
P
and equilateral. If the distance from point P to
point Q is 15 meters, what is the perimeter of the garden?
1. ________
Q
2. The drama department at Mountlake Terrace HS
has built a stage floor in the shape of a regular octagon.
The length of each side of the octagon is 4 yards.
__
If CD is the apothem, what is the approximate area
of the stage floor? (round to nearest tenth)
3. What is the perimeter of the
regular octagon shown to the right?
What is the approximate area?
(round to the nearest tenth)
2.________
3. P =______
4 cm
4.6 cm
4.6 cmA
4. Find the approximate area of a regular hexagon with apothem 3 3 .
Draw the figure. (round to the nearest tenth)
A = ______
4. __________
5. Mrs. Smith wants to add a triangular deck in the yard behind her
house. Each side is to be 18 feet long. Find the length of the railing
that will fit completely around the deck. Then find the area of the deck.
5. __________
6. Sam is building a pen for dogs near the barn. The pen will be a
hexagon with sides of 3 yards. Find the area of the pen.
6. __________
One of the most famous buildings in the United States is the
Pentagon in Arlington, Virginia, where the Defense Department
is located. The Pentagon has approximately 23,000 employees,
and is virtually a city in itself with private restaurants, a bank,
a heliport, and a television station. This tremendous office
complex has 17.5 miles of corridors. Each outer wall of the
building is 921 feet long. Pentagon ABCDE represents the
outer edge of the building with point F at its center. The
smaller pentagon represents the courtyard that lies within the
Pentagon Building.
7. What is the perimeter of the Pentagon Building?
8. What is the measure of the central angle
? What type of triangle is
?
9. Find the length of ̅̅̅̅ . Round your result to the one decimal place.
10. Find the total area of the Pentagon building. Round your result to one decimal place.
11. The inner pentagon that represents the courtyard has a side length of approximately 307
feet. Find the area of the courtyard.
12. What is the approximate ratio of the side length of the courtyard to the pentagon
Building?
13. What is the approximate ratio of the area of the courtyard to the area of the Pentagon
Building?