Question

A parallelogram has sides A, B, C, and D. Sides A and B have a length of `5` and sides C and D have a length of `3`. If the angle between sides A and C is `pi/3`, what is the area of the parallelogram?

Answer 1

`15\sqrt{3}/2` square units.

Explanation:

The area of a parallelogram is the product of two adjacent sides times the sine of the angle between them.

Hence area is `5xx3xxsin(pi/3)=15sqrt3/2` square units

(For a given parallelogram, there are two possible values for the angle, but these are supplementary to each other and thus have the same sine. Also `sin(pi-theta)=sintheta`)