The Pentagon houses the  United States Department of Defense at its Arlington, Virginia, location.  Each face of the Pentagon measures 921 feet in length and the apothem of the building measures 783.449 feet. What is the area of the first floor and the interior courtyard (the area inside of the pentagonal shape)? Round your answer to the nearest square foot.

A. 360,778 square feet
Incorrect. Remember to multiply the entire perimeter of the pentagon.

B. 901,946 square feet
Incorrect. Check your calculations in your formula to be sure that you multiplied by ½ , the apothem and the total perimeter.

C. 1,803,891 square feet
Correct! Using the given information you found the area of the office space and courtyard of just the 1st floor of the Pentagon!

D. 3,607,783 square feet
Incorrect. Do not forget to multiply by ½ in the formula.

Safe-T-Signs is a company that manufactures stop signs for roadways. In order to be efficient, the company cuts the stop signs out of large circular sheets of aluminum that have a radius of 8 feet. The largest stop signs that are manufactured have a side length of 36 inches, and an apothem of 43.456 inches. What is the maximum number of large stop signs that can be cut out of 1 circular sheet of aluminum?

A. 3
Incorrect. Be sure to make sure the circle units are in inches.

B. 4
Correct! Excellent work finding the area of 1 octagon and then dividing that number into the area of the 8 foot radius circle.

C. 5
Incorrect. Although your answer was larger than 4, the extra that is left over cannot make a complete octagon shaped stop sign.

D. 6
Incorrect. Make sure that you find the total area of the octagon and used the entire perimeter in your calculations.

Mariella is putting new tile in her house. Each tile is a square with 4 inscribed circles and a side length of 20 inches. She has estimated that she will need 104 tiles to finish the room. Which answer below is closest to the total area of the red shaded region in the entire room?

A. 85.84 square inches
Incorrect. Be sure to include all 104 tiles from the entire room in finding the total area of the red shaded area.

B. 8168.14 square inches
Incorrect. Once you have found the area of the 4 circles, subtract that from the total area of the square to find the remaining (red color) area.

C. 8927.44 square inches
Correct! Great job using subtraction to find the remaining area on one tile, and then multiplying by 104.

D. 32672.56 square inches
Incorrect. Be careful in your calculations. Once you have found the area of all four circles, subtract that from the total area of 1 tile before multiplying by 104.

A honeycomb structure made by honeybees is in the shape of a series of hexagonal prisms. The base of each cell in the honeycomb is in the shape of a regular hexagon as shown in the picture below.

If the side length of each hexagon is approximately 1.5 centimeters, what is the approximate area of one hexagon in the honeycomb structure?

A. 0.98 centimeters
Incorrect. The formula for the area of a regular polygon is A = 1 2 Pa, where P represents the perimeter of the hexagon. 1.5 centimeters is the side length not the perimeter of the hexagon.

B. 3.38 centimeters
Incorrect. To determine the length of the apothem of the hexagon, use a 30-60-90 special right triangle. The apothem is equal to the long leg of the 30-60-90 triangle.

C. 5.85 square centimeters
Correct!

D. 11.69 centimeters
Incorrect. The length of the apothem is equal to 1 2 Pa, of the side length times √3.

Jessica is using a roll of tape to trace a circle within a circle, or concentric circles. She created the concentric circles by tracing the outside of the roll, and then the inside of the roll. The diameter of the larger outer circle is 20 centimeters and the diameter of the inner circle is 15 centimeters. Which answer below is closest to the area of the space between the circles? Round your answer to the nearest thousandth.

A. 137.445 cm²
Correct! Great job subtracting the two areas to find the area of the space between the circles.

B. 145.299 cm²
Incorrect. Check the order of your formulas. Be sure to subtract the area of the smaller circle from that of the larger circle.

C. 7.854 cm²
Incorrect. Be sure you square the radius in your formulas.

D. 43.75 cm²
Incorrect. The formula for the area of a circle must contain the radius squared multiplied by pi.