ANSWER
66.3 (no units included)
EXPLANATION
We want to find the area of the figure given.
The figure is a semi-circle.
The area of a semi-circle is half the area of a circle. Therefore, the area of a semi-circle is:
[tex]A=\frac{1}{2}\cdot\pi\cdot r^2[/tex]where r = radius.
We are given the diameter of the semi-circle to be 13 mm.
The diameter is twice the radius, which means that the radius is:
[tex]\begin{gathered} r=\frac{1}{2}\cdot d \\ \Rightarrow r=\frac{1}{2}\cdot13 \\ r=6.5\text{ mm} \end{gathered}[/tex]Therefore, the area of the semi-circle is:
[tex]\begin{gathered} A=\frac{1}{2}\cdot3.14\cdot6.5^2 \\ A=66.3mm^2 \end{gathered}[/tex]That is the area of the semi-circle.