A parallelogram is a quadrilateral with opposite sides that are both equal and parallel. Unlike a rectangle, the angles in a parallelogram aren't necessarily 90°, but opposite angles are equal, and adjacent angles are supplementary. Parallelograms form the basis for many concepts in geometry and physics.
Total length around the parallelogram:
\[ P = 2(a + b) \]
where:
The sum of adjacent interior angles is always supplementary:
\[ \alpha + \beta = 180^\circ \]
where:
Height can be calculated using sine of an angle and adjacent side:
\[ h = a \sin(\alpha) = a \sin(\beta) \]
where:
Relationship between the diagonals \(m\) and \(n\):
\[ m^2 + n^2 = 2(a^2 + b^2) \]
where:
The space enclosed by the parallelogram:
\[ A = b \times h = a \times b \sin(\alpha) \]
where: