Question

Two opposite sides of a parallelogram each have a length of `4`. If one corner of the parallelogram has an angle of `(5 pi)/8` and the parallelogram's area is `24`, how long are the other two sides?

Answer 1

Other two sides are `color(green)(6.4944)` long each

Explanation:

Given : `AD = BC = a = 4, /_A = theta = (5pi)/8, Area A_p = 24`

To find `AB = CD = b`

Area of parallelogram is `A_p = AD * BB’ = a * h`

But `h = AB sin /_A = b * sin theta`

Hence, A_p = a * b * sin theta#

`b = A_p / (a * sin theta) = 24 / (4 * sin ((5pi)/8)) = color (green)(6.4944)`