Perimeter and Area - Area of a Parallelogram

A parallelogram is a four-sided flat shape (quadrilateral) where the opposite sides are parallel and equal in length. Visually, it looks like a rectangle that has been tilted or 'pushed' to one side.

The 'Base' ($b$) of a parallelogram can be any of its four sides. In diagrams, it is usually the side shown at the bottom, represented by a solid horizontal line.

The 'Height' ($h$) is the perpendicular distance from the base to the opposite parallel side. Visually, this is often represented by a dashed vertical line dropped from a top vertex to the base (or an extension of the base), forming a $90^{\circ}$ angle marked with a small square symbol.

The area of a parallelogram is the region enclosed within its four sides. If you visually cut a triangle from one side of the parallelogram and slide it to the other side, the shape transforms into a rectangle. This shows that the area of a parallelogram is identical to the area of a rectangle with the same base and height.

It is crucial to use the 'corresponding height' for a specific base. If a parallelogram has two different pairs of parallel sides, each pair has its own specific perpendicular distance (height) between them.

Area is always expressed in square units, such as $cm^{2}$ or $m^{2}$, representing how many small unit squares would fit inside the shape.

A single diagonal divides a parallelogram into two congruent triangles of equal area. Consequently, the area of each triangle is exactly $\frac{1}{2}$ the area of the parallelogram: $\text{Area of Triangle} = \frac{1}{2} \times b \times h$.