Suppose a parallelogram has sides of length a and b. Is this enough information to compute the area of the parallelogram? If not, what additional information is required?

No. it's not enough

Step-by-step explanation:

1) No. it's not enough

2) To compute the area of a parallelogram it's necessary the height of the parallelogram, i. e. a perpendicular line segment from the base up to its parallel side.

3) Because a parallelogram is made up by two triangles and the area of it is calculated using the height. Then to cover the area of a parallelogram it's mandatory to calculate the height, the perpendicular distance between their horizontal sides.