# The Area of any Irregular Quadrilateral

A plane figure bounded by four straight line segments is called an irregular quadrilateral. The area of any irregular quadrilateral can be calculated by dividing it into triangles.

__Example__:

Find the area of a quadrilateral whose sides are m, m, m and m respectively and the angle between the first two sides is a right angle.

__Solution__:

From the figure we notice that is a right-angled triangle, in which m, m. Also

Now, the area of m

In , m, m, m

m

Now,

The area of the quadrilateral area of area of

The area of the quadrilateral square meters.

__Example__:

In a quadrilateral the diagonal is cm and the two perpendiculars on it from the other vertices are cm and cm respectively. Find the area of the quadrilateral.

__Solution__:

Given that from the figure m, m, m

The area of area of area of

The area of square meters.