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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?

 

 Mar 25, 2021
 #1
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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

 

 

cool cool cool

 Mar 25, 2021

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