¶ 2025 AMC 12B Problem 12
¶ Problem:
The windshield wiper on the driver's side of a large bus is depicted below.
Arm pivots back and forth around point , sweeping out an arc of , symmetric about the vertical line through . The wiper blade is attached to at its midpoint and stays vertical as the arm moves. The arm is feet long, and the wiper blade is feet tall. What is the area of windshield cleaned by the wiper, in square feet, to the nearest hundredth? (Assume that the windshield is a flat vertical surface.)
Answer Choices:
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¶ Solution:
The original area swept by the windshield wiper is shown below.
The idea is that we can transform this region into a rectangle without changing its area by moving some of the area in the top curved region into the bottom curve region. The new resulting region is depicted in red in the diagram below.
Hence, the original area is equal to the area of the red rectangle. Since the red rectangle has height and base , it has an area of exactly , and so the answer is .
The problems on this page are the property of the MAA's American Mathematics Competitions