fbpx

Area of Quadrilateral

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 (m2).

About a Quadrilateral

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

Properties of a quadrilateral are:

  • 4 vertices and 4 sides.
  • Sum of interior angles = 360o
  • Can generally have sides of different lengths and angles of different measures.

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

Examples of Quadrilaterals
Examples of Quadrilaterals (Source)

Derivation of Area of Quadrilateral

Area of Quadrilateral

In the above quadrilateral, h1 and h2 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

QuadrilateralsAreas
Area of Square(Side)2
Area of rectangleLength * breadth
Area of kite\(\frac{1}{2}\) * Product of diagonals
Area of parallelogram\(\mbox{base} * \mbox{height}\)
Area of trapezium\(\frac{\mbox{base}_1 + \mbox{base}_2}{2} * \mbox{height}\)

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
h1 = 5cm
h2 = 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 = 180cm2.

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

Leave a Comment

Your email address will not be published. Required fields are marked *

Scroll to Top