ANSWER
[tex]10.5 + 7.25\pi \: {units}^{2} [/tex]
EXPLANATION
The figure is made up of a triangle and a semicircle.
The area of the triangle is
[tex] = \frac{1}{2} \times base \times height[/tex]
[tex] = \frac{1}{2} \times 7 \times 3[/tex]
[tex] = \frac{21}{2} [/tex]
[tex] = 10.5 \: units \: square[/tex]
The area of the semicircular part is
[tex] = \frac{\pi \: {d}^{2} }{8} [/tex]
We can find the diameter squared using the Pythagoras Theorem.
[tex] {d}^{2} = {7}^{2} + {3}^{2} [/tex]
[tex] {d}^{2} = 49+ 9[/tex]
[tex] {d}^{2} = 58[/tex]
We substitute this into the formula for finding the area of the semicircle to get;
[tex] = \frac{58\pi}{8} [/tex]
[tex] = 7.25\pi \: {units}^{2} [/tex]
Therefore the area of the figure is
[tex]10.5 + 7.25\pi \: {units}^{2} [/tex]
See diagram in attachment.
