
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).
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b) Find AB (in cm).
Choose:
c) Find the exact area of ΔABC (in square cm).
Choose:



2. 
Given square ABCD with a diagonal length of 24 inches.
a) Find the measure of ∠CAD.
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b) Find PQ (in inches).
Choose:



c) Find the exact area of ABCD (in square inches.).
Choose:


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



c) Find the exact area of ABCDEF (in square feet).
Choose:


4. 
Given regular pentagon ABCDE with side length of 10 cm.
a) Find PQ to the nearest tenth of a cm.
Choose:
b) Using your answer from part a, find the area of ABCDE to the nearest cm^{2}.
Choose:

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:

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.
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6. 
The apothem of a regular polygon is half of the side of the polygon. What is the name given to this polygon?
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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.



Choose:


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:



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