Area of a Parallelogram
📐 What is a Parallelogram?
A parallelogram is a quadrilateral (4-sided polygon) in which both pairs of opposite sides are parallel and equal in length.
- Opposite sides are parallel: $AB \parallel DC$ and $AD \parallel BC$
- Opposite sides are equal: $AB = DC$ and $AD = BC$
- Opposite angles are equal
- Diagonals bisect each other
Common examples include rectangles, rhombuses, and squares — all of which are special types of parallelograms.
🔑 The Area Formula
$$ A = b \times h $$
where $b$ = length of the base and $h$ = perpendicular height (altitude)
Key Definitions:
- Base ($b$): Any one of the sides of the parallelogram. You can choose any side as the base.
- Height ($h$): The perpendicular distance between the base and its opposite side. This is NOT the slant side!
⚠️ Common Mistake: Students often confuse the slant side with the height. The height must always be measured at a 90° angle to the base. The slant side is only equal to the height in a rectangle.