In the figure, the area of quadrilateral ABCD is

×
32

×
33

×
34

×
35

✓
36
In the figure, the area of quadrilateral ABCD is
32
33
34
35
36
Since \triangle ABD is a right triangle,
BD = \sqrt{3^2+4^2} =5
\because 13^2 = 12^2+5^2 =169
The measure of three sides of \triangle BCD has the following relationship
BC^2 = BD^2+CD^2
Therefore, \triangle BCD is also a right triangle.
So the area of quadrilateral ABCD is,
A_{ABCD} =A_{\triangle ABD }+A_{\triangle BCD }
=\dfrac{1}{2}\cdotp 3\cdotp 4+\dfrac{1}{2}\cdotp 5\cdotp 12
=36