Two ways to measure a parallelogram
When to use base times height versus the sides-and-angle formula, and how the angle quietly controls a parallelogram's area.
The base and height method
The most direct area formula is base times perpendicular height. It works because a parallelogram can be cut along a vertical line and rearranged into a rectangle with the same base and height, so the two shapes share an area. The catch is that the height must be measured straight across from the base to the opposite side, at a right angle, not along the slanted edge. When you have a clean height measurement, this method is fast and needs no trigonometry.
The sides and angle method
Sometimes you know the two side lengths and the angle where they meet but not the height. In that case the area equals side A times side B times the sine of the included angle. The sine term is really the height in disguise, because side B times the sine of the angle is exactly the perpendicular height dropped onto side A. This mode has a bonus: knowing both sides lets it also report the perimeter, which the base-and-height mode cannot.
How the angle controls the area
For fixed side lengths, the angle between the sides decides how much area the parallelogram encloses. At 90 degrees the shape is a rectangle and the area is largest, since the sine of 90 degrees is 1. As the angle leans toward 0 or 180 degrees the parallelogram flattens, the sine shrinks toward zero, and the area collapses even though the sides never change length. That is why a slanted parallelogram always has less area than a rectangle built from the same two sides.
Choosing the right mode for your problem
Pick base-and-height when a diagram gives you the perpendicular height directly, such as a textbook figure with the height drawn in. Reach for sides-and-angle when you have measured the edges and the corner angle, which is common in surveying, drafting, and physics problems involving vectors. If you only need the area and have the height, the first mode is simplest. If you also want the perimeter, the second mode delivers both numbers at once.