How to Calculate the Area of Quadrilateral

If the diagonal and the lengths of the perpendiculars taken from the vertices are known, the area of the quadrilateral may be determined as follows: Area=12 × diagonal length×sum of the length of the perpendicular . 

A quadrilateral is a closed shape with four line segments defining it. Regular or irregular quadrilaterals exist. A regular quadrilateral is one in which all four sides are the same length. An irregular quadrilateral is a quadrilateral which is not regular.

Area of Quadrilateral

The area of a quadrilateral is defined as the area enclosed by the quadrilateral’s sides. It’s measured in square units like m2,cm2, in2and so forth. The method for calculating the area of a quadrilateral is dependent on the type of quadrilateral and the information available. If the quadrilateral does not belong to one of the kinds listed above, we can find its area by dividing it into two triangles or by using the method for obtaining the area of a quadrilateral with four sides (called the Bretschneider′s formula). The formulas for calculating the area of a quadrilateral that does not fit into any of the usual categories may be found here.

Area of a quadrilateral formula 

Dividing into two triangles:

 Area=12 ×d×(h1+h2)

Area of Quadrilateral Formula Using Sides

The Bretschneider formula can be used to calculate the area of a quadrilateral when the sides and two opposite angles are known. Consider a quadrilateral with sides a,b,c and d and opposing angles 1 and 2.

Area of a quadrilateral= s-as-bs-cs-d-abcθ/2

Here s is the semi perimeter semi perimeter=(a+b+c+d)/2

And θ= 1+2

Area of Quadrilateral Using Heron’s Formula

according to Heron’s formula. Using Heron’s formula,  we can compute the area of a quadrilateral.

Area of a triangle having 3 sides is given as: Area= ss-as-bs-c

Here s is the semi perimeter and it is given as s=(a+b+c)/2

Using a diagonal, split it into two triangles (Use the diagonal whose length is known).

To find each triangle’s area, use Heron’s formula.

The quadrilateral’s area is calculated by adding the areas of two triangles.

Area of a Quadrilateral Examples

Quadrilaterals and their area have many practical applications in the realms of design, agriculture, and architecture. The notion is extremely beneficial in the sophisticated creation of navigation maps that are precisely scaled to actual distances and areas. The number of unit squares that can fit inside a quadrilateral determines its area.

Example

Calculate the area of a quadrilateral whose diagonal is 15 cm and sum of height of two triangle is 12cm.

Solution.

The area of a quadrilateral is given as Area=12 ×diagonal ×(sum of height of two triangle)

So Area=12 ×12 ×15

 Area=90 cm2

 What is a quadrilateral?

A quadrilateral is a closed shape produced by uniting four points, any three of which are non-collinear in geometry. A quadrilateral is made up of four sides, four angles, and four vertices. The term “quadrilateral” comes from a Latin phrase that means “four sides” and “quadra.” A quadrilateral’s four sides may or may not be equal. A polygon with four sides, four angles, and four vertices is called a quadrilateral. When naming a quadrilateral, it’s important to remember the vertices’ order.

Quadrilateral Properties

Each of the quadrilaterals mentioned above has its unique set of characteristics. However, there are several qualities that all quadrilaterals share. The following are the details.

• There are four sides to them.

• There are four of them.

• They are divided into two diagonals.

• All interior angles add up to 360 degrees.

Convex, Concave and Intersecting Quadrilaterals

The measurements of the angles and lengths of the sides of quadrilaterals are used to classify them. All of these forms of quadrilaterals have four sides, and the sum of their angles is 360 degrees, as the term “quad” means “four.”

Another way to categorise quadrilaterals is to use the following terms:

• Quadrilaterals that are totally contained within a figure are known as convex quadrilaterals.

• Concave Quadrilaterals have at least one diagonal that extends partially or completely outside of the figure.

• Intersecting Quadrilaterals are not simple quadrilaterals with non-adjacent sides that intersect. Self-intersecting or crossed quadrilaterals are a type of quadrilateral that intersects itself.

Conclusion

We see a lot of closed figures with four sides that are varied shapes, lengths, and widths. Quadrilaterals make up those four-sided figures. A quadrilateral, then, is a basic closed plane shape with four sides. Quadrilaterals of various shapes have diverse qualities, and some of these properties make them unique. However, the sum of all quadrilaterals’ interior angles will be the same. Quadrilaterals include squares, rectangles, parallelograms, rhombuses, trapeziums, and kites. The area of a quadrilateral is given as Area=12 ×diagonal ×(sum of height of two triangle)

A trapezium is a quadrilateral with only one set of parallel opposed sides. The bases of the trapezium are its parallel sides. It’s median is the line segment that connects the midpoints of non-parallel sides.