Answer:
- courtyard: 217,800 ft²
- building: 1,241,263 ft²
Explanation:
You want the area of the courtyard and the building at the Pentagon, given the measures shown in the figure. The area of the courtyard is about 5 acres.
Courtyard
An acre is 43560 ft², so the courtyard area is ...
(5 ac)(43560 ft²/ac) = 217,800 ft² . . . . courtyard area
Pentagon
The drawing shows the area of the building divided into a trapezoid and a triangle. The trapezoid has bases 921 ft and 1490 ft, and height 876 ft.
The triangle has a base of 1490 ft and a height of 541 ft.
The areas of these figures can be found using the formulas for area of a trapezoid and a triangle. The area of the building and courtyard will be the sum of these areas.
The total area here is ...
A = trapezoid area + triangle area
A = 1/2(921 +1490)(876) +1/2(1490)(541) = 1,459,063 . . . . square feet
Building
The area of the building is the difference between the total area of the pentagon and the area of the courtyard:
building area = 1459063 -217800 = 1,241,263 . . . . square feet
The area of the building is about 1,241,263 square feet.
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Additional comment
If you use the formula for the area of a pentagon based on its side length, you find the total area to be about 1459379.5 square feet. This is about 316.5 square feet more than computed using the triangle and trapezoid dimensions.
A = √(5(5+2√5))/4s² . . . . where s=921 ft.
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