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Quadrilateral calculator
Want to know the area of your quadrilateral room for furnishing? Or even if you need to solve the geometry problems for your next class, check out this quadrilateral calculator.
This online tool helps you calculate the area of a quadrilateral with much ease. It doesn’t matter if don’t know which type of quadrilateral you are dealing with. Just fill in the required fields and it will calculate area of your quadrilateral.
Are you excited to know about quadrilaterals? Because, we are going to explain how to find quadrilateral area using our calculator, quadrilateral definition and its types, formula of quadrilateral area, and how can you calculate quadrilateral area by yourself.
How to use quadrilateral calculator?
By using above irregular quadrilateral calculator, you can easily find out area of quadrilateral without any efforts. It saves your time and assists you in calculating quadrilateral area.
To use this calculator, follow the below steps:
- Select the option for which you want to calculate the quadrilateral.
- Select the set of parameters that are given.
- Enter the given values in the respective input boxes.
- Hit the Calculate button to get the result of calculation.
It instantly calculates the area and also provides each step of the calculation with formula. So, it doesn’t only calculates the area, but also helps you prepare the topic for your class or exams.
What is a quadrilateral?
In Euclidean plane geometry, a quadrilateral is a polygon with four sides or edges and four corners or vertices. Wikipedia.
Or quadrilateral can be defined simply as:
In geometry, a quadrilateral can be defined as a two-dimensional, closed shape which has four straight sides.
Properties of a quadrilateral
Followings are the quadrilateral properties.
- The sum of all the interior angles of a quadrilateral is 360°.
- A quadrilateral has 4 vertices, 4 angles, and 4 sides.
- A quadrilateral can be regular or irregular.
What are different types of quadrilateral?
There are several types of quadrilateral shapes in geometry. Some of those are listed below in the table with pictures.
Name of the Quadrilateral: | Picture of Quadrilateral: | Properties of the Quadrilateral: |
Parallelogram | Opposite sides are parallel. Opposite sides are equal. Opposite angles are equal. | |
Kite | Consecutive sides are equal. Pair of diagonally opposite angles are equal. Diagonals meet each other at 90°. | |
Square | All sides are equal. All angles are equal of 90°. | |
Isosceles trapezoid | Both bases are parallel. Opposite sides are equal. Angles are congruent. | |
Rectangle | Opposite sides are parallel. Opposite sides are equal. All angles are equal and measure 90°. | |
Rhombus | All sides are equal. Opposite angles are equal. | |
Trapezoid | Opposite sides are parallel. Adjacent angles add up to 180°. |
All the above shapes that we see in our daily life are quadrilateral. You may be wondering about the method to calculate area of any of the above quadrilaterals. Don’t worry! We have got you covered.
We have rectangle area calculator, rhombus area calculator, trapezoid area calculator, parallelogram area calculator, kite area calculator, or square calculator, if you want to calculate the area of a specific quadrilateral.
Quadrilateral formula
Area of quadrilateral formula can be divided into three categories based on given values. Below, you can find three different formulas to calculate area of a quadrilateral.
1. When diagonals and angle between them are given
If diagonals and angle between those diagonals are given, the quadrilateral area formula for that case can be expressed as:
Area = \(p \times q \times \sin(angle)\)
Where:
p and q represent the diagonals.
2. When bimedians and angle between them are given
If bimedians and angle between them are known, area of quadrilateral can be calculated by using the following formula:
Area = \(m \times n \times \sin(angle)\)
Where:
m and n represent the bimedians.
Note: Bimedians are the lines which link to the centers of the opposite sides.
3. When two opposite angles and four sides are given
If two opposite angles and four sides are known, area of quadrilateral can be calculated by using the Bretschneider's formula.
Area = \(√[(s - a) \times (s - b) \times (s - c) \times (s - d) - a \times b \times c \times d \times cos2 (0.5 \times (angle1 + angle2))]\)
Where:
a, b, c, and d represent quadrilateral sides,
s represents the expression (\(0.5 \times (a + b + c + d)\)) which is a semi perimeter, angle1 and angle2 represent two opposite angles of quadrilateral.
How to find the area of a quadrilateral?
Area of quadrilateral can be calculated by using any of the above formula depending on the given values. You may want to measure the area of your backyard or lawn and facing difficulties to get the equations right. Well, you can always use our above calculator for that purpose.
Here we will go through the complete process to calculate quadrilateral area. Follow the steps below to fin the area of a quadrilateral:
- Write down the given values.
- Write down the relevant formula from above.
- Substitute the values in the formula and calculate the area of your quadrilateral.
Example:
Calculate the area of a quadrilateral having two sides of 6 cm and 4 cm respectively with 30° angle?
Solution:
Step 1:
Write down the given values.
p = 6 cm, q = 4 cm, angle = 30°
Step 2:
Write down the relevant formula from above.
Area = \(p \times q \times \sin(angle)\)
Step 3:
Substitute the values in the formula and calculate the area of your quadrilateral.
Area = \(6 \times 4 \times \sin (30°)\)
Area = \(24 \times 0.5\)
Area = \(12 cm^2\)
So, a quadrilateral with two sides of 6 cm and 4 cm, and an angle of 30° will have area of 12 cm^{2}.
FAQs
What is the formula of area of quadrilateral ABCD?
The area of quadrilateral ABCD can be stated as:
Area of quadrilateral ABCD= ½ d (h_{1}+h_{2})
What is the formula of the area of quadrilateral?
The following are the quadrilateral formulas.
1. When diagonals and angles are given
Area = \(p \times q \times \sin(angle)\)
p and q are the diagonals.
2. When bimedians and angles are given
Area = \(m \times n \times \sin(angle)\)
m and n are bimedians.
3. When opposite angles and all sides are given
Area = \(√[(s - a) \times (s - b) \times (s - c) \times (s - d) - a \times b \times c \times d \times cos2 (0.5 \times (angle1 + angle2))]\)
a, b, c, and d are quadrilateral sides, angle1 and angle2 represent two opposite angles of quadrilateral, and s represents the expression (0.5 × (a + b + c + d)) which is a semi perimeter.
How do you find the area of an irregular quadrilateral?
Follow the below steps to calculate area of an irregular quadrilateral.
- Split the irregular quadrilateral into two triangles by drawing a diagonal.
- Compute the area of the triangle whose angle is known.
- Find the length of the diagonal with the Law of Cosines.
- Find the area of the second triangle using Heron's Formula.
- Now, add the area of both triangles, which will give you the area of irregular quadrilateral.
What is the perimeter and area of quadrilateral?
Here is the area and perimeter of various quadrilaterals.
Quadrilateral formulas | Rectangle | Square | Parallelogram | Rhombus | Trapezium |
Area | \(l \times b\) | \(a^2\) | \(l \times h\) | \(½ \times d1 \times d2\) | \(½ \times (Sum of parallel sides) \times height\) |
Perimeter | \(2 \times (l + b)\) | \(4a\) | \(2 \times (l + b)\) | \(4a\) | Sum of all the sides |
What is an example of an irregular quadrilateral?
An irregular quadrilateral comprises of the sides that are not equal. Some examples of irregular quadrilaterals are:
- Rectangle
- Parallelogram
- Kite
- Rhombus
- Trapezoid
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