A quadrilateral is any polygon with four sides, four vertices, and four interior angles. The sum of interior angles in any quadrilateral is always 360°. Quadrilaterals are classified by their side lengths, angle measures, and whether sides are parallel.
A parallelogram has two pairs of parallel sides. Opposite sides are equal in length, and opposite angles are equal. Consecutive angles are supplementary (add to 180°). The area is A = base × height. Special parallelograms include the rectangle (all angles are 90°), the rhombus (all sides are equal), and the square (all angles are 90° and all sides are equal). A square is simultaneously a rectangle, a rhombus, and a parallelogram.
A trapezoid has exactly one pair of parallel sides (called bases). The non-parallel sides are legs. The area formula is A = ½(b₁ + b₂) × h, where b₁ and b₂ are the two parallel bases and h is the perpendicular height between them. An isosceles trapezoid has equal legs and equal base angles. A right trapezoid has two right angles along one leg.
A kite has two pairs of adjacent sides that are equal (not opposite sides). The diagonals of a kite are perpendicular, and exactly one pair of opposite angles is equal. The area of any quadrilateral whose diagonals are perpendicular can be calculated as A = ½ × d₁ × d₂. This formula also applies to rhombuses and squares.