To find the total area of the figure we have to find the area of the semicircle, then the area of the rectangle and the area of the triangle and add them up.
In order to do this we have to identify the radius of the semicircle. The radius is 1/2 the diameter, and the diameter is the height of the rectangle. So the radius is 2cm.
Then the base of the triangle is 10cm minus the length of the rectangle, 6cm. So the base of the triangle is 4cm.
The area of a semicircle is one half the area of a circle.
The area of a circle is
So the area of the semicircle is:
![A_(semicircle)=(1)/(2)\pi\cdot r^2=(\pi)/(2)\cdot2^2=2\pi\approx6.28\operatorname{cm}^(2)]()
The area of the rectangle is:
![A_(rec\tan gle)=length* height=6\operatorname{cm}*4\operatorname{cm}=24cm^2]()
And the area of the triangle is:
![A_(triangle)=(base* height)/(2)=\frac{4\operatorname{cm}*4\operatorname{cm}}{2}=8\operatorname{cm}^2]()
Finally, the total area of the figure is:
![\begin{gathered} A_(total)=A_(semicircle)+A_(rec\tan gle)+A_(triangle)=6.28\operatorname{cm}+24\operatorname{cm}+8\operatorname{cm}^(2) \\ A_(total)=38.28\operatorname{cm}^(2) \end{gathered}]()
The total area of the figure is 38.28cm² (rounded to the nearest hundredth)