# Area of Quadrilateral Calculator

Table of contents

What is a quadrilateral?Quadrilateral area formula and calculating irregular quadrilateral areaArea of common types of quadrilateralHow to use this area of quadrilateral calculatorOther related calculatorsFAQsOur area of quadrilateral calculator will help you to determine the **area** of any **quadrilateral** with different known parameters. This article will briefly discuss quadrilaterals and the different **quadrilateral area formulae** available. So join us below to learn how to find the area of a quadrilateral.

## What is a quadrilateral?

Q: How do you define a quadrilateral?

A: "Four points joined by straight lines."

Q: But what if the points are *collinear*?

A: "The points have to be non-collinear."

Q: But what if the lines don't form a *closed figure*?

A: * A quadrilateral is a closed figure (a polygon) with four sides*.

You can see quadrilaterals everywhere, from swimming pools and soccer fields to buildings and bridges. Recognizing the geometry of a structure will greatly simplify calculations. There are many types of quadrilaterals, such as rectangles and trapezoids. To estimate the latter's area quickly, you can head to Omni's trapezoid calculator. Let's first learn how to calculate the area of an irregular quadrilateral.

## Quadrilateral area formula and calculating irregular quadrilateral area

There are various methods to calculate the area of an irregular quadrilateral based on which parameters are known:

1. From **four sides** and **two opposite angles**:

*A = √((s - a)(s - b)(s - c)(s - d) - a · b · c · d · cos ^{2}(δ · γ))*

where:

*A*—**Area**of the quadrilateral;*s*— The**semi-perimeter**of the quadrilateral, equal to*0.5 · (a + b + c + d)*;*a, b, c, d*— The**four sides**of the quadrilateral; and*δ, γ*— Any**two opposite angles**of the quadrilateral.

2. From its **diagonals** and the **angle** between them:

*A = 0.5 · e · f · sin(α)*

where:

*e, f*— The lengths of the**two diagonals**of the quadrilateral; and*α*— The**angle between the two diagonals**. There are two unique angles between the two diagonals,*α*and*(π-α)*. Since*sin(π-α) = sin(α)*, the quadrilateral area formula yields the same result for both angles.

3. From the **bimedians** and the **angle** between:

*A = m · k · sin(θ)*

where:

*m, k*— The lengths of the**two bimedians**of the quadrilateral; and*θ*— The**angle between the two bimedians**. Again, since*sin(π-θ) = sin(θ)*, we can use this formula to calculate quadrilateral area irrespective of our choice of angle.

4. From the **Cartesian coordinates** of the quadrilateral's **vertices**:

*A = 0.5 · (x _{1}y_{2} - y_{1}x_{2} + x_{2}y_{3} - y_{2}x_{3} + x_{3}y_{4} - y_{3}x_{4} + x_{4}y_{1} - y_{4}x_{1})*

where *(x _{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3}), (x_{4}, y_{4})* are the

**coordinates**of the

**four vertices**of the quadrilateral.

## Area of common types of quadrilateral

We've seen how to find the area of a quadrilateral with an irregular shape. For quadrilaterals like squares and rectangles, other simpler formulae for area exist:

1. **Rectangles**: A quadrilateral whose opposite sides are equal in length, and all angles are right angles.

Its area is given by:

*A = b · a*

where:

*b*— The rectangle's**length**; and*a*— The rectangle's**breadth**.

2. **Square**: A quadrilateral with all sides equal in length, and all its angles are right angles.

Its area is given by:

*A = a ^{2}*

where *a* is the square's **side** length.

3. **Parallelogram**: A quadrilateral whose opposite sides are equal in length and parallel to each other, and the opposite angles are equal.

The formula for a parallelogram's area is:

*A = b · h*

where:

*b*— The parallelogram's**base**; and*h*— The parallelogram's**height**(the perpendicular distance between the base and its opposite side).

4. **Rhombus**: A quadrilateral whose four sides are equal in length.

Its area is given by:

*A = 0.5 · d _{1} · d_{2}*

where *d _{1}, d_{2}* are the rhombus's

**diagonals**.

5. **Trapezoid**: A Trapezoid (or trapezium) is a quadrilateral with at least one pair of parallel sides.

The area of a trapezoid is:

*A = 0.5 · h · (a + b)*

where:

*a, b*— The lengths of the**parallel sides**of a trapezoid; and*h*— The trapezoid's**height**.

6. **Kite**: A kite is a quadrilateral in which two pairs of adjacent sides are equal in length.

Its area is given by:

*A = 0.5 · d _{1} · d_{2}*

where *d _{1}, d_{2}* are the kite's

**diagonals**.

## How to use this area of quadrilateral calculator

Our area of quadrilateral calculator is a powerful tool capable of calculating the area of any quadrilateral from different known parameters:

**Select**the**type**of the**quadrilateral**. Choose`unknown`

for irregular quadrilaterals.- For irregular quadrilaterals, you can choose which
**parameters**are`given`

. **Enter**the parameters in their respective fields with proper units.- This area of a quadrilateral calculator will instantly calculate the answer for you.

### What is the area of a square with side 5 cm?

**25 cm ^{2}**. To calculate this, follow these steps:

**Multiply**the square's side by itself to get`A = 5 × 5 = 25`

.- Verify your result with our area of a quadrilateral calculator.

### What is the sum of all the angles in a quadrilateral?

The sum of all the angles in a quadrilateral is **360°** or **2π radians**. Think of a quadrilateral as a fusion of two triangles that share a common side (the diagonal).