A simple closed four sided figure is known as a Quadrilateral.

**Parallelogram:**In a parallelogram, opposite sides are parallel and congruent.

Area = length * height

Perimeter = 2 (length + breadth)**Rectangle:**In a rectangle, opposite sides are parallel and congruent.

Area = length * breadth

Diagonal of the rectangle = √(l^{2}+ b^{2})

Area = length * breadth

Perimeter = 2 (length + breadth)**Square:**All sides and angles of a square are congruent.

Length of the diagonal = l √2 (where l is the length of the side of a square)

Area = (Side)^{2}

Perimeter = 4 X side**Rhombus:**All sides and all opposite angles of a rhombus are congruent. Also, the diagonals are perpendicular to and each other.

Area = (a*b)/2 (where a and b are the lengths of the diagonals of a rhombus)

Perimeter = 4 * length**Trapezium:**No sides, angles and diagonals of a trapezium are parallel to each other.

Area = (1/2)h*(L+L_{2})

Perimeter = L + L_{1}+ L_{2}+ L_{3}

- Of all the quadrilaterals of the same perimeter, the one with the maximum area is the square.
- The quadrilateral formed by joining the midpoints of the sides of any quadrilateral is always a parallelogram (rhombus in case of a rectangle, rectangle in case of a rhombus and square in case of a square).
- The quadrilateral formed by the angle bisectors of the angles of a parallelogram is a rectangle.
- For a rhombus □ABCD, if the diagonals are AC and BD, then AC
^{2}+ BD^{2}= 4 * AB^{2}. - If a square is formed by joining the midpoints of a square, then the side of the smaller square = side of the bigger square/√2.
- If P is a point inside a rectangle □ABCD, then AP
^{2}+ CP^{2}= BP^{2}+ DP^{2}. - The segment joining the midpoints of the non-parallel sides of a trapezium is parallel to the two parallel sides and is half the sum of the parallel sides.
- For a trapezium □ABCD, if the diagonals are AC and BD, and AB and CD are the parallel sides, then AC
^{2}+ BD^{2}= AD^{2}+ BC^{2}+ 2 * AB * BD. - If the length of the sides of a cyclic quadrilaterals area, b, c and d, then it's area = √(s-a)(s-b)(s-c)(s-d) , where s is the semi - perimeter.
- The opposite angles of a cyclic quadrilateral are supplementary.

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- The sides a
_{n}of regular inscribed polygons, where R is the radius of the circumscribed circle = a_{n}= 2R sin^{180o/n} - Area of a polygon of perimeter P and radius of in-circle r = (P*r)/2
- The sum of the interior angles of a convex POLYGON, having n sides is 180
^{o}(n - 2). - The sum of the exterior angles of a convex polygon, taken one at each vertex, is 360
^{o}. - The measure of an exterior angle of a regular n- sided polygon is 360
^{o}/n . - The measure of the interior angle of a regular n-sided polygon is (n-2)180
^{o}/n - The number of diagonals of in an n-sided polygon is n(n-3)/2