Question

Two opposite sides of a parallelogram have lengths of `8`. If one corner of the parallelogram has an angle of `pi/8` and the parallelogram's area is `32`, how long are the other two sides?

Answer 1

Other two sides are of `10.45 (2dp)` units length.

Explanation:

Let ABCD be the parallelogram of which opposite sides AB=CD=8 and altitude "h" from perpendicular drawn from point D on side AB at E. We know area of parallelogram `=AB*h :. 32=h*8 or h=32/8=4` Now on the right angled triangle AED `/_A=pi/8=22.5^0 ; DE=h=4`
`:.sin22.5= 4/(AD) or AD = 4/sin22.5 = 10.45 (2dp) units = BC` [Ans]