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?
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Answer:
338 squared inches is the approximate area of the window that is not cleaned by the wiper.
Step-by-step explanation:
Area of trapezoid shaped widow: A
Length of the longer side of window= a = 42 inches
Another length of window = b = 32 inches
height of the window = h = 20 inch
Area of trapezoid = [tex]\frac{(a+b)}{2}\times h[/tex]
[tex]A=\frac{42 inch+32 inch}{2}\times 20 inch[/tex]
[tex]A=740 inch^2[/tex]
Area of the semicircle = A'
Radius of the circle = r = 16 inch
Area of the semi-circle = [tex]\frac{1}{2}\pi r^2[/tex]
[tex]A'=\frac{1}{2}\times 3.14\times (16 inch)^2=402.12 inch^2[/tex]
Area of the window left uncleaned :
= A - A' = [tex]740 inch^2-402.12 inch^2=337.88 inch^2\approx 338 inch^2[/tex]
338 squared inches is the approximate area of the window that is not cleaned by the wiper.