Quadrilateral Formulas: Types and Properties

A four-sided polygon with a total interior angle of 360 degrees is known as quadrilateral. Quadrilaterals are divided into several categories, including square, rectangle, parallelogram, rhombus, and trapezoid. The area of the quadrilateral is calculated using five distinct formulas. 

There are usually just 5 formulas, though some of them have modifications and can be used for several purposes — for example, the rhombus formula can be used to compute the area of a kite and vice versa. However, understanding the various types of quadrilaterals and their attributes is necessary before learning all of a quadrilateral's formulas.

Also Read: Pair of Linear Equations in Two Variables Formula

Quadrilaterals: Types and Properties with Formulas

Quadrilateral figures are available in a wide range of sizes and shapes. Many more quadrilaterals may be simply drawn, and we can even recognize many of them around us.

Rectangle

A rectangle is a quadrilateral with parallel and equal opposite sides.

Properties of a Rectangle

• All of the angles are correct.
• The diagonals are equal in length and cross each other (divide each other congruently).
• At the intersection of two diagonals, opposite angles are formed.

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Important formulas for Rectangles

If we assume that a rectangle's length is L and its width is B, then

• Diagonal length = \(\sqrt{L2}\)+B
• Area of Rectangle = L × B
• Rectangle’s perimeter = 2(L+B)

Squares

A square is a quadrilateral, or a special type of parallelogram, with all of its sides equal.

Properties of Squares

• All of the sides and angles are identical.
• The diagonals are parallel.
• Parallel sides are those that are opposite each other.
• The diagonals cross each other and are perpendicular.
• Angles that are perpendicular to each other are said to be congruent.

Important Formulas for Squares

• If we assume that the length of a square is L, then the diagonal length is L √2.
• L2 is the area of a square.
• A square's perimeter is equal to 4L.

Rhombus

A quadrilateral with four equal-length sides is known as a rhombus. Because of its characteristic of equality of length, it is also known as an equilateral quadrilateral.

Properties of a Rhombus

• All sides are of equal length.
• Angles that are perpendicular to each other are said to be congruent.
• The diagonals meet at a point where they are perpendicular to one another.
• Supplementary angles are created by adjacent angles (For e.g., ∠m + ∠n = 180°).

Important Formulas for a Rhombus

• If we consider the lengths of a rhombus to be m and n of its diagonals, then
• (m*n) / 2 = Area of a Rhombus
• A rhombus' perimeter is equal to 4L.

Trapezium

A trapezium is a quadrilateral having at least one pair of parallel sides that is convex in shape.

Properties of a Trapezium

• The trapezium's bases are parallel to one another i.e. (MN ? OP).
• If the non-parallel sides are congruent, so will the diagonals.
• There are no identical sides, angles, or diagonals.

Important Formulas for a Trapezium

• Trapezium's area MNOP = (1/2) h (M+N) parallel sides 
• Trapezium perimeter = M + N + O + P
• Trapezoid area = 1/2 x sum of parallel sides x height
• 1/2 x sum of parallel sides = area of trapezium's median

(As a reminder, the median is the line that runs parallel to the parallel sides at the same distance.)

 Isosceles Trapezium

An isosceles trapezium is a quadrilateral with just one pair of opposite sides parallel to one another and all other pairs of sides congruent.

Properties of an Isosceles Trapezium

• Two neighboring angles are supplementary, meaning that they sum up to 180 degrees.
• It's possible to engrave it in a circle.
• As the base, the diagonals form a pair of congruent triangles with equal sides.
• The sum of the four exterior and four interior angles equals four right angles.
• We get a fragment of a cone by rotating an isosceles trapezium around the vertical axis that connects the midpoints of the parallel sides.

Important Formula of an Isosceles Trapezium

• MNOP = h (M+N)/2 is the area of an isosceles trapezium.
• Isosceles trapezium perimeter = m + n + 2o

Parallelogram

A quadrilateral with opposite parallel sides is known as a parallelogram (and therefore opposite angles equal).

Properties of a parallelogram

• Parallel sides are those that are opposite each other.
• The opposing sides are congruent.
• Angles that are perpendicular to each other are said to be congruent.
• Interior angles on the same side (consecutive angles) are supplementary.
• Angles A and B are supplementary, as angles D and C.
• A parallelogram is divided into two congruent triangles by each of its diagonals.
•  A parallelogram's diagonals are bisected by each other.

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Important Formula of a parallelogram

• Area = Base × Height

Points to Remember

• A rectangle's diagonals are equal in length and cross each other (divide each other congruently).
• The opposite sides of a square are called parallel sides.
• Adjacent angles form supplementary angles in a rhombus.
• The diagonals of a trapezium will be congruent if the non-parallel sides are congruent
• An isosceles trapezium's surrounding angles are supplementary, meaning they add up to 180 degrees.
• A parallelogram's diagonals are divided in half by one another.