D. 20.34
In this case, we must calculate first the Areas of the Triangle ([tex]A_{t}[/tex]), in square units, and the Circle ([tex]A_{c}[/tex]), in square units, later we subtract the Area of the former from the Area of the latter to determine the Area of unshaded region ([tex]A_{u}[/tex]), in square units. The Area formulas for each figure are, respectively:
Triangle
[tex]A_{t} = \frac{1}{2}\cdot b\cdot h[/tex] (1)
Circle
[tex]A_{c} = \pi\cdot r^{2}[/tex] (2)
Unshaded Area
[tex]A_{u} = A_{c} - A_{t}[/tex] (3)
Where:
[tex]h[/tex] - Height of the triangle.
[tex]b[/tex] - Base of the triangle.
[tex]r[/tex] - Radius of the circle.
If we know that [tex]h = 10[/tex], [tex]b = 5[/tex] and [tex]r = 3.8[/tex], then the area of the unshaded region is:
[tex]A_{t} = \frac{1}{2}\cdot (5)\cdot (10)[/tex]
[tex]A_{t} = 25[/tex]
[tex]A_{c} = \pi\cdot 3.8^{2}[/tex]
[tex]A_{c} \approx 45.365[/tex]
[tex]A_{u} = 45.365-25[/tex]
[tex]A_{u} = 20.365[/tex]
The correct answer is D.
Please see this question related to Area problems: https://brainly.com/question/16151549
