Quadrilaterals can be defined as, types of polygons that have four sides, four vertices, and four angles along with a pair of diagonals. The Sum of interior angles of quadrilaterals is 360°. There are various kinds of quadrilaterals. As the name itself suggest the word is a combination of two Latin words ‘Quadri‘ means a variant of four, and ‘latus‘ means side.

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Kinds of Quadrilaterals


One of the examples of a concave quadrilateral is a Dart. It is a quadrilateral with bilateral symmetry like a kite, but with a reflex interior angle.

Convex Quadrilaterals

Quadrilaterals which have all four interior angle less than 180° are called concave quadrilaterals. There are various types of Convex Quadrilaterals:TrapeziumKiteParallelogramRectangleRhombusSquare

Trapezium

A trapezium is a quadrilateral which has one pair of opposite sides parallel. In a regular trapezium, non-parallel sides are equal and its base angles are equal.Trapezium1

Kite

Kite has two pairs of equal adjacent sides and one pair of opposite angles equal. Diagonals of kite intersect perpendicularly. The longest diagonal of the kite bisects the smaller one.Kite

Parallelogram

A quadrilateral whose opposite sides are equal and parallel is called a Parallelogram. Opposite angles of a Parallelogram are equal and its diagonals bisect each other.

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Sample Problems on Quadrilaterals

Now let us see some problems based on quadrilaterals :Problem 1: Perimeter of quadrilateral ABCD is 46 units. AB = x + 7, BC = 2x + 3, CD = 3x – 8, and DA = 4x – 6. Find the length of the shortest side of the quadrilateral.Solution: