Quadrilateral is a closed convex polygon bounded by four sides. We have already seen that the quadrilaterals are classified according to the interior angles and the sides. Therefore, the names of the quadrilaterals vary according to their properties. Areas of rectangle, square, parallelograms can be found by the suitable formulas derived. If we are given a quadrilateral whose sides or angles are unequal, we can find the areas by splitting it into triangles which do not overlap.

Hence in this section let us see different methods of finding the areas of quadrilaterals.

Quadrilateral : A quadrilateral is a closed figure bounded by four sides. What is area? Area is the amount of space occupied by a plane figure.

Area of a Quadrilateral:
(1) Since a diagonal divides a quadrilateral into two non-overlapping triangles, we can say that the area of a quadrilateral is the sum of the areas of each triangle.
Area of Quadrilateral
In the above Quadrilateral TRUE, the diagonal TU divides it into two triangles, $\Delta TRU$ and $\Delta TEU$.
Area of the Quadrilateral TRUE = Area of $\Delta TRU$ + Area of $\Delta TEU$

= $\frac{1}{2}$ x TU x h1 + $\frac{1}{2}$ x TU x h1

= $\frac{1}{2}$ x TU x [h1 + h2]


(2) If we are given the length of one of the diagonal and the length of each side of the quadrilateral we can find the area of the quadrilateral by finding the area of each triangle using Heron's Formula which is $\sqrt{s\;(s-a)\;(s-b)\;(s-c)\;}$

Quadrilateral Area

(3) Parallelogram : Area of a parallelogram = Base x Height

(4) Rectangle : Area of a rectangle = length x width

(5) Square : Area of a Square = side x side

(6) Trapezoid : Area of a Trapezoid = $\frac{1}{2}$ x Height x [sum of the parallel sides]

= $\frac{1}{2}$ x h x (a + b)

(7) Rhombus : Area of a Rhombus = $\frac{1}{2}$ x Diagonal1 x Diagonal2