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 cars 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 Wh class=

Respuesta :

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 = [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.