Your car's back window is in the shape of a trapezoid with the dimensions shown. The 16 -inch window wiper cleans a part of the window in a semicircular pattern. What is the approximate area of the window that is not cleaned by the wiper? CLEAR CHECK about 3.8 square inches about 398 square inches about 402 square inches about 800 square inches
To find the area of the window that is not cleaned by the wiper, we need to find the area of the trapezoid and subtract the area of the semicircle.
The formula to find the area of a trapezoid is:
Area = (1/2) * (base1 + base2) * height
The trapezoid has a height of 16 inches, base1 of 12 inches, and base2 of 20 inches.
Area of the trapezoid = (1/2) * (12 + 20) * 16 = 16 * 16 = 256 square inches
The wiper cleans a part of the window in a semicircular pattern. To find the area of the semicircle, we need to use the formula:
Area of a circle = (π * radius^2) / 2
The radius of the semicircle is half the width of the window, which is the average of the two bases of the trapezoid.
Radius = (12 + 20) / 2 = 16 inches
Area of the semicircle = (π * 16^2) / 2 = (π * 256) / 2
Now, let's calculate the area of the window that is not cleaned by the wiper:
Area = Area of the trapezoid - Area of the semicircle
Area = 256 - (π * 256) / 2
Using an approximation of π as 3.14:
Area ≈ 256 - (3.14 * 256) / 2
Area ≈ 256 - 402.88 / 2
Area ≈ 256 - 201.44
Area ≈ 54.56 square inches
The approximate area of the window that is not cleaned by the wiper is about 54.56 square inches.
Therefore, the closest option is "about 54.6 square inches", but that is not given as an option.