We are given a rhombus with one side measuring 5 cm, and one angle measuring 50 degrees. To determine the area we can use the following formula:
[tex]A=a^2sin\alpha[/tex]Where "a" is one side and alpha is the measure of any interior angle of the rhombus. In this case, we have that
[tex]\angle\text{ODC}=50^0[/tex]Since line DB bisects the angle ADC, that means that:
[tex]\angle ADC=2(50^0)=100^0[/tex]Replacing in the formula for the area:
[tex]A=(5\operatorname{cm})^2\sin 100[/tex]Solving we get:
[tex]A=24.62cm^2[/tex]