# Quadrilateral Area Formulas

Quadrilateral area formulas are used to calculate the area of a closed figure that has four sides, called a quadrilateral. There are different types of quadrilateral depending upon the properties of different parameters. We will learn the quadratic area formulas in the upcoming sections.

## What are Quadrilateral Area Formulas?

Different quadrilateral area formulas are used for different quadrilaterals depending upon their types. These different types of quadrilaterals are square, rectangle, parallelogram, rhombus, kite, trapezoid, and many more. Here, we will see the formulas for areas of parallelogram, square, trapezoid, rectangle, and kite.

Area of quadrilateral formula when it is divided into separate triangles as shown in the image below:

In the above figure, we have two triangles BCD and ABD

On calculating the areas of triangles separately,

The area of the triangle BCD = (1/2) × d × \(h_1\)

The area of the triangle ABD = (1/2) × d × \(h_2\)

The area of the quadrilateral ABCD = Sum of areas of ΔBCD and ΔABD.

Thus, the area of the quadrilateral ABCD = (1/2) × d × \(h_1\) + (1/2) × d × \(h_2\) = (1/2) × d × (\(h_2\) + \(h_2\)).

Thus, the area of the quadrilateral formula when one of its diagonals and the heights of the triangles (formed by the given diagonal) are given is, Area = (1/2) × Diagonal × (Sum of heights)

## List of Quadrilateral Area Formulas

Let us see the table consists of a list of area formulas for various types of quadrilaterals.

Name of Quadrilateral |
Area of Quadrilateral Formulas |
---|---|

Square |
Area of a square formula = (side) |

Rhombus |
Area of a rhombus formula = (1 ⁄ 2) × product of diagonals |

Kite | Area of a kite formula = (1 ⁄ 2) × product of diagonals |

Parallelogram |
Area of a parallelogram formula = base × height |

Rectangle |
Area of a rectangle formula = length × breadth |

Trapezoid |
Area of a trapezoid formula = 1/2 × (sum of the lengths of parallel sides) × height |

**Note: Please note that all rhombus can be considered kites but all kites are not rhombus**.

## Examples on Quadrilateral Area Formulas

Let us consider a few illustrations based on the quadrilateral area formulas in this solved examples section.

**Example 1:** Noah measured the sides of the square as 9 m, what would be the area of a square?

**Solution:**

To find: The area of a square.

Given:

Side of the square = 9 m

Using quadrilateral area formulas,

Area of a Square formula = (side)^{2}

Area of a Square = (9)^{2}

Area = 81 m^{2}

Therefore, the area of a square is 81 m^{2}.

**Example 2:** If you walk around a trapezoidal park that has one base measuring 200 m and the length of the other base is 100m, with height of the trapezoid shape as 50m, what is the area of that trapezoidal park?

**Solution:** To find: The area of a trapezoidal park.

One base of a park = 200 m

Second base of a park = 100 m

Height of a park = 50 m

Using quadrilateral area formulas,

Area of a Trapezoid = 1/2 × (Sum of the lengths of parallel sides) × height

= 1/2 × 300 × 50

= 150 × 50

= 7500 m^{2}

Therefore, the area of the trapezoidal park is 7500 m^{2}.

**Example 3:** The base length of a parallelogram is 7 units and the height is 9 units. Using the quadrilateral area formula of parallelogram find its area.

**Solution:**

To find the area of a quadrilateral

Given:

Base = 7 units, Height = 9 units

Using quadrilateral area formula of parallelogram

Area of parallelogram formula = Base × height

Area = 7 × 9

Area = 63 units^{2}

Therefore, the area of the quadrilateral is 63 square units.

## FAQs on Quadrilateral Area Formulas

### What Is the Quadrilateral Area Formula for Parallelogram?

The area of a parallelogram is defined as the amount of space covered by a parallelogram in a two-dimensional plane. A parallelogram is a special kind of quadrilateral. It is a four-sided quadrilateral whose area formula is expressed as, product of its base and height, i.e., A = base × height square units.

### What Is the Quadrilateral Area Formula for Rectangle?

The area of a rectangle is the number of unit squares covered within the boundary of the rectangle. It is rectangle is a four-sided quadrilateral with opposite side as equal. Its area formula is expressed as product of its length and breadth, i.e., A = length × breadth square units.

### What Is the Quadrilateral Area Formula for Square?

The area of a square is the measure of the space or surface occupied by it. It is a four-sided quadrilateral with all sides equal, whose area formula is equal to the product of the length of its two sides, i.e., A = (side)^{2} square units.

### What Is the Quadrilateral Area Formula for Rhombus?

A rhombus is a four-sided quadrilateral whose area formula is equal to half the product of the lengths of the diagonals. The formula to calculate the area of a rhombus when diagonals are given is expressed as

Area of a rhombus = (1 ⁄ 2) × product of diagonals square units.

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