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?

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 class=

Verified Answer :

The answer is 337.88 in2

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 = \(\frac{(a+b)}{2}\times h\)

\(A=\frac{42 inch+32 inch}{2}\times 20 inch\)

\(A=740 inch^2\)

Area of the semicircle  = A'

Radius of the circle = r = 16 inch

Area of the semi-circle = \(\frac{1}{2}\pi r^2\)

\(A'=\frac{1}{2}\times 3.14\times (16 inch)^2=402.12 inch^2\)

Area of the window left uncleaned :

= A - A' = \(740 inch^2-402.12 inch^2=337.88 inch^2\approx 338 inch^2\)

338 squared inches is the approximate area of the window that is not cleaned by the wiper.