Find the area of a quadrilateral ABCD in which AB = 3cm, BC = 4cm, CD = 4cm, DA = 5cm and AC = 5cm.

In the quadrilateral ABCD,

we have,

We have, AB = 3cm, BC = 4cm, CA = 5cm

We have,

(By Pythagoras theorem)

=

Hence,

Now in

AC = 5cm, CD = 4cm, DA = 5cm

We know that,

Now, Area of triangle

=

(Since, Heron's formula [area =

=

=

=

Since,

Area of

(Since, Area of triangle =

=

Area of quadrilateral ABCD = Area of

Hence from (ii) and (iii),

Area of quadrilateral ABCD =