A parking lot is to have the shape of a parallelogram that has adjacent sides measuring 281 feet and 253 feet. The angle between the two sides is 57°. What is the area of the parking lot? Round to the nearest integer.
A) 59,624 square feet
B) 29,812 square feet
C) 31,008 square feet
D) 38,720 square feet

Question

Quizplus · Accepted Answer

The area of a parallelogram is given by the formula $ \text{Area} = b \times h $, where $ b $ is the base and $ h $ is the height. However, when the height is not given directly but an angle between the base and the adjacent side is given, the area can also be calculated using the formula $ \text{Area} = ab \sin(C) $, where $ a $ and $ b $ are the lengths of the adjacent sides and $ C $ is the included angle. In this case, $ a = 281 $ feet, $ b = 253 $ feet, and $ C = 57^\circ $. Thus, the area is $ 281 \times 253 \times \sin(57^\circ) $, which rounds to 59,624 square feet when calculated.

A Parking Lot Is to Have the Shape of a Parallelogram