Area of quadrilateral = ?
The area of the general quadrilateral can be obtained by dividing the quadrilateral into two triangles by drawing one its diagonals. The area of the quadrilateral is obtained by adding the areas of the two triangles.
In the given figure, the quadrilateral is divided into two triangle by drawing the diagonal AC. Let
and
be the lengths of the altitudes drawn from B and D on the diagonal AC.
Area of ΔABC =
Area of ΔADC =
Area of the quadrilateral ABCD = Area of ΔABC + Area of ΔADC
∴ Area of the quadrilateral ABCD =+=
Thus, Area of the quadrilateral =
× Length of the diagonal × Sum of the length of the altitudes from the opposite vertices to the diagonal.