Practice Page
Directions: Grab a paper and pencil to make your computations.

1.
Given equilateral triangle ABC with an apothem of length 3 cm.
a) Find AP (in cm).
Choose:
4
6
6rad3
9

b) Find AB (in cm).
Choose:
3rad3
6
6rad3
9

c) Find the exact area of ΔABC (in square cm).
Choose:
9rad3
18rad3
27rad3
54rad3

pa1

 

 

2.
Given square ABCD with a diagonal length of 24 inches.
a) Find the measure of ∠CAD.
Choose:
30º
45º
60º
75º

b) Find PQ (in inches).
Choose:
6rad2
12rad2
12rad3
6rad3

AA2
 
c) Find the exact area of ABCD (in square inches.).
Choose:
144
144rad2
288
288rad2

 

 

3.
Given regular hexagon ABCDEF with a side length of 8 feet.
a) Find AP (in feet).
Choose:
8
8rad3
4
4rad3

b) Find PQ (in feet).
Choose:
4
4rad3
6rad3
8rad3
AA3
 

c) Find the exact area of ABCDEF (in square feet).
Choose:
192
54rad3
96rad3
192rad3

 

 

4.
Given regular pentagon ABCDE with side length of 10 cm.
a) Find PQ to the nearest tenth of a cm.
Choose:
5.0
6.5
6.9
7.1

b) Using your answer from part a, find the area of ABCDE to the nearest cm2.
Choose:
173
178
345
355
AA4
Hint: Use Trig.

 

 

5.
The US Pentagon is a regular pentagon whose outer walls are each 921 feet in length.
a) Find the area, to the nearest square foot, covered by this enormous building, including the center courtyard.
Choose:
633,824 sq. feet
789,354 sq. feet
1,459,379 sq. feet
1,578,425 sq. feet

uspentagon
US Pentagon, Arlington, Virginia, headquarters of the US Department of Defense.
Photo courtesy of NASA global software.
 
b) Find the distance, to the nearest foot, from the west entrance, A, to the eastern vertex point, B. Assume A is the base of the apothem.
Choose:
921 ft.
1,148 feet
1,250 feet
1417 feet

 

 

6.
The apothem of a regular polygon is half of the side of the polygon. What is the name given to this polygon?
Choose:
equilateral triangle
square
regular pentagon
regular hexagon

 

 

7.
Honey bee nests, called honeycombs, are constructed to form hexagonal grids. The cells measure 5 mm from vertex to vertex. The illustration at the right shows 36½ cells. Assuming the cells to be regular hexagons, find the area of the cells shown in the illustration, to nearest square mm.
honeybees
  Choose:
65 mm2
592 mm2
1369 mm2
2371 mm2

 

 

8.
The minimum size of a stop sign is a regular octagon measuring 30 inches across. Find the area of this stop sign to the nearest tenth of a square inch.
Choose:
745.6 square inches
2172.8 square inches
543.2 square inches
4345.6 square inches
stopsign

 

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