How would I find area cleaned?

Question

windsheild wiper arm 16 inches long
wiper only 12 inches long
the windsheild wiper moves through a 50 degree angle?

what formula should I use?

Answer 1

You have an area bounded by a sector of a 16 inch circle, a sector of a 4 inch circle, and a 50 degree angle.
Figure 50/360 pi (R^2- r^2)
That is,
50/360 pi (16^2) is the area of the sector swept by the arm.
50/360 pi (4^2) is the area of the sector not covered by the gap between the wiper and the base of the arm, so subtract this.
Simplify the formula and you get what I've written above.
Plug in ..
50/360 pi ((16^2) - (4^2)) and that will give you the area cleaned.