Geometry Quadrilaterals

A quadrilateral is a four-sided polygon. The five main quadrilateral types (listed in order from most to least symmetric) are: squares, rectangles, parallelograms, rhombuses, and trapezoids. Each type of quadrilateral has its own defining features and equations to determine the area and the perimeter. The interior angles for all quadrilaterals must sum to 360°.

Square

All sides are equal in length

All angles are right (i.e., 90°)

Opposite sides are parallel

Perimeter = 4(side)

Area = (side)²

Rectangle

Opposite sides are equal in length

Opposite sides are parallel

All angles are right (i.e., 90°)

Perimeter = 2(width) + 2(length)

Area = (length)(width)

Parallelogram

Opposite sides are equal in length

Opposite sides are parallel

Opposite angles are equal (i.e., bottom-right = upper-left)

Adjacent angles are supplementary

Perimeter = 2(width) + 2(length)

Area = (width)(height)

Rhombus

All sides are equal in length

Adjacent angles are supplementary

Opposite angles are equal

Diagonals form right angles

Diagonals bisect each other

Diagonals bisect end angles

Note: In a rhombus, while all sides are equal, all angles are not necessarily equal.

Perimeter = 4(side)

Area = 1/2(diagonal₁ × diagonal₂)

Trapezoid

One pair of sides is parallel

Perimeter = A + B + C + D

Area = 1/2(height)(base₁ + base₂)