The area of quadrilateral is generally defined as the region occupied inside the boundaries of a quadrilateral or a flat object or figure.

The area is measured in square units. The standard unit is square meters (m^{2}).

Index

**About a Quadrilateral**

A quadrilateral is a 4-sided polygon whose sum of interior angles is equal to 360^{o}.

Properties of a quadrilateral are:

- 4 vertices and 4 sides.
- Sum of interior angles = 360
^{o} - Can generally have sides of different lengths and angles of different measures.

Examples of a quadrilateral are square, rectangle, parallelogram, trapezium, rhombus, and kite.

**Derivation of Area of Quadrilateral**

In the above quadrilateral, h_{1} and h_{2} are heights of the triangles ABC and ADC respectively. BE and DF are perpendicular to the diagonal AC.

Now,

area(quad ABCD) = area(△ABC) + area(△ADC)

area(△ABC) = \(\frac{(\mbox{base * height})}{2} = \frac{(AC*h_1)}{2}\)

area(△ADC) = \(\frac{(\mbox{base * height})}{2} = \frac{(AC*h_2)}{2}\)

⇒ area(quad ABCD) = \(\frac{(AC*h_1)}{2} + \frac{(AC*h_2)}{2} = AC \left( \frac{h_1 + h_2}{2} \right) = \frac{1}{2}*AC*(h1+h2)\)

**∴ Area of Quadrilateral = \(\frac{1}{2}\) * Diagonal * Sum of Heights of Two Triangles**

**Areas of Different Quadrilaterals**

Quadrilaterals | Areas |

Area of Square | (Side)^{2} |

Area of rectangle | Length * breadth |

Area of kite | \(\frac{1}{2}\) * Product of diagonals |

Area of parallelogram | \(\mbox{base} * \mbox{height}\) |

Area of trapezium | \(\frac{\mbox{base}_1 + \mbox{base}_2}{2} * \mbox{height}\) |

Area of Rhombus | \(\frac{1}{2} diagonal_1 \cdot diagonal_2\) |

**Solved Example**

**Question.** In the above-given quadrilateral ABCD, what is the area of ABCD if diagonal AC = 24cm and heights are 5cm and 10cm respectively?

**Solution.** Given,

AC = 24cm

h_{1} = 5cm

h_{2} = 10cm

Sum of heights = 5 + 10 = 15cm

Hence area(quad ABCD) = \(\frac{1}{2}\) * Diagonal * Sum of height of two triangles

= \(\frac{1}{2} * 24 * 15 = 12 * 15 = 180cm^2\)

∴ Area of quad ABCD = 180cm^{2}.

**FAQs**

**What is the area of a quadrilateral formula?**Area of quadrilateral = \(\frac{1}{2}\) *Diagonal * Sum of height of two triangles

**What are the different examples of quadrilaterals?**Examples of quadrilaterals are squares, rectangles, parallelograms, etc.

**How to find the area of a quadrilateral?**The area of a quadrilateral is calculated by adding the areas of the two triangles that essentially combine to give the quadrilaterals.

Read More:

1. Area of an Octagon

2. Area of a Pentagon