Two long strips of paper are each $2$ inches wide, and they overlap so that the angle between the strips is $20^{\circ}$. What is the number of square inches in the area of the parallelogram formed by the overlap?
+128473 We can slpit the paralllelogram in half such that we form two isosceles triangles with the apex angle = 160°
The sides are all equal and we can find the length of one (= s) as
2 / sin 20° = s / sin 90
s = 2 /sin 20°
Area =
s^2 * sin (160°) =
( 2 / sin 20°)^2 * sin (160°) = 11.7 in^2
