 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 formula 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.

### Types of Quadrilaterals and Their Properties with Formulas

1. Rectangle

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

Properties of a Rectangle

• All are 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, then

Length of the diagonal = √ [L2 + B2]

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 a square = L2.

The perimeter of a 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 suppose the lengths of a rhombus be m and n of the diagonals of a rhombus, then

Area of a rhombus = (m× n) / 2

The perimeter of a rhombus = 4L

4. Trapezium

a convex quadrilateral with minimum 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 other i.e. (MN ⫽ OP).

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

• No sides, angles, and diagonals are similar

Important Formulas for a Trapezium

Area of a trapezium MNOP = (1/2) h (M+N) {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 linking 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

Example1

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.

Solution1

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

Area = [Base 1 + Base 2]/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

Example2

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?

Solution2

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

1. Can we find the area of the quadrilateral using the Triangle Area Formula?

Ans. Yes, we can use the triangle area formula to compute the area of the quadrilateral. Imagine a quadrilateral named MNOP. Think of a straight line from the corner between ‘m’ and ‘n’ to the corner between ‘o’ and ‘p’. This line would divide the quadrilateral into two triangles. Seeing that the area of a triangle is MN sinO, where O is the angle between sides m and n, you can apply this formula twice (once for each of your fictional triangles) in order to compute the total area of the quadrilateral.

2. What is the formula to compute the area of a quadrilateral using the Triangle Area Formula?

Ans. For any quadrilateral with sides L1, L2, L3, L4, the area of quadrilateral formula =

= 0.5 L1 × L 4 × sin(Side 1&4 angle) + 0.5 × L2 × L3 × sin (Side 2 & 3 angle) or

Area = 0.5 m × p × sin m + 0.5 × n × n × sin N

You have the sides as (16, 10, 8, 5) and angles (45, 80) you need, so let's solve:

= 0.5 (16 × 10) × sin (45) + 0.5 × (8 × 5) × sin (80)

= 80 × sin (45) + 20 × sin (80)

= 80 × 0.707 + 20 × 0.984

= 56.56 + 19.68 = 76.24 square inches