Quadrilateral Formula

There are typically 5 formulas that you can consider to compute the area of the 7 most common types of quadrilaterals. There are typically only 5 formulas though some of them have variations and can be applied for double duty — for example, you can calculate the area of a kite with the rhombus formula and vice-e-versa. However, before beginning to know all formulas of a quadrilateral, it is important to understand the types of quadrilaterals and their properties

Below are all types of figures that are known as quadrilaterals. You can easily draw many more quadrilaterals and we can even recognize many around us.

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Types of Quadrilaterals and Their Properties with Formulae

1. Rectangle

The quadrilateral that has its opposite sides parallel and equal is called a rectangle.

Properties of a Rectangle:

• All are at right angles.

• The diagonals measure equal and intersect each other (divide each other congruently).

• Opposite angles are created at the point where diagonals meet are similar

Important Formulas for Rectangles:

• If we suppose the length of a rectangle is L and breadth is B, the length of the diagonal = \[\sqrt{ L^{2} + B^{2} }\]

• Area of Rectangle = L × B

• Perimeter of Rectangle = 2(L+B)

2. Squares

The quadrilateral or say a special type of parallelogram that has all its sides equal is called a square.

Properties of Squares:

• All sides and angles are identical to one another

• Opposite sides are parallel

• The diagonals are in congruence

• The diagonals are perpendicular to and intersect each other.

Important Formulas for Squares:

If we suppose the length of a square is L then,

• The length of the diagonal = L √2

• Area of square = L×L.

• The perimeter of square = 4L

3. Rhombus

A quadrilateral whose four sides are all congruent in length is a rhombus. Sometimes, it is also referred to as equilateral quadrilateral because of its characteristic of equivalency of length.

Properties of a Rhombus:

• All sides are of the same length

• Opposite angles are in congruence

• The diagonals are perpendicular to and intersect each other.

• Adjacent angles make for supplementary angles (For e.g., ∠m + ∠n = 180°).

Important Formulas for a Rhombus:

If we assume the lengths of a rhombus be L  and m, n be the length of  its diagonals then,

• Area of rhombus = (m× n) / 2

• The perimeter of rhombus = 4L

4. Trapezium

A convex quadrilateral with a minimum of one pair of parallel sides is called a trapezium in English and referred to as trapezoid in American and Canadian

Properties of a Trapezium:

• The bases of the trapezium are parallel to one another.

• If the non-parallel sides are in congruence then diagonals will be too.

Important Formulas for a Trapezium:

• Area of a trapezium MNOP =  (M+N)/2 h {M and N are parallel sides}

• Perimeter of a trapezium = M + N +O + P

• Area of the trapezoid = 1/2 x sum of parallel sides x height

• Area of Median of trapezium = 1/2 x sum of parallel sides

Reminder: the median is the line that is at an equal distance from the parallel sides).

5. Isosceles Trapezium

The quadrilateral with only one pair of opposite sides parallel to each other and other pairs of sides are congruent then it is an isosceles trapezium.

Properties of an Isosceles Trapezium:

• Two pairs of adjacent angles are supplementary i.e. add up to 180 degrees.

• Can be inscribed in a circle.

• The diagonals form a pair of congruent triangles with equal sides as the base

• The sum of the four exterior angles as well as the four interior angles is 4 right angles.

• We obtain a crumb of a cone by rotating an isosceles trapezium about the vertical axis that links the midpoints of the parallel sides

Important Formula of an Isosceles Trapezium:

• Area of an isosceles trapezium MNOP = h (M+N)/2

• Perimeter of an isosceles trapezium = M + N + 2O

Solved Examples 

Example 1: Find out the area of the trapezoid using the length and the height of its bases. You have a trapezoid with one base of 8 cm, another base of 12 cm, and the line of height joining them is 4cm long.

Solution:

Given the length of the trapezoid as well as the height of both bases, we will use the following formula:

Area = (Base1+Base2)/2 × height

or

A = (m + n) / 2 × h

Now, do the math and make the equation

You can calculate its area like this: (8 + 12)/2 × 4 = (20)/2 × 4 = 40cm

Example 2: Find the area of a kite with the following measures. The kite has diagonals with lengths of 18 meters and 6 meters, then what is its area?

Solution:

We will apply the rhombus diagonal formula to find the area of a kite since rhombus is a special kind of kite with all lengths of a similar measure.

Use the kite-like, rhombus diagonal formula as below:-

Area = (Diag. 1 × Diag 2.)/2

We get (18 × 6) / 2

108/2 = 54square meters

Note: Diagonals are the straight line segments in between two opposite corners on the kite.