The formula for the area of a rectangle is
A=l*w
plug in the data we know
A=10*16
A=160cm²
Now for the semicircle. The formula for the area of a circle is
A=πr²
But a semicircle is half that, since it's half of a circle so we can use
A=1/2πr²
plug in the data we know
A=1/2π8²
A=1/2π64
A=32π
A=100.53cm²
Add the two areas together
160+100.53=260.53cm²
So the answer is 260cm²