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).
Index
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](https://protonstalk.com/wp-content/uploads/2021/05/Quadrilaterals.png)
Derivation of Area of Quadrilateral
![Area of Quadrilateral](https://protonstalk.com/wp-content/uploads/2021/05/Quadrilateral.png)
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
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
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
Area of quadrilateral = \(\frac{1}{2}\) *Diagonal * Sum of height of two triangles
Examples of quadrilaterals are squares, rectangles, parallelograms, etc.
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