Given that h=10, b=5, and r=3.8, find the area of the unshaded region. use 3.14 for π as necessary. all answers are expressed in square units.
a. 70.34
b. 36.93
c. 25
d. 20.34

D. 20.34

In this case, we must calculate first the Areas of the Triangle (), in square units, and the Circle (), in square units, later we subtract the Area of the former from the Area of the latter to determine the Area of unshaded region (), in square units. The Area formulas for each figure are, respectively:

Triangle

(1)

Circle

(2)

Unshaded Area

(3)

Where:

- Height of the triangle.

- Base of the triangle.

- Radius of the circle.

If we know that , and , then the area of the unshaded region is:

The correct answer is D.

Please see this question related to Area problems: link

The area of the circle is found using the formula Area = PI x r^2

The area of a triangle is found using the formula Area = 1/2 x base x height.

Using the given dimensions:

Area of the circle = 3.14 x 3.8^2 = 45.3416 square units.

The area of the triangle is 1/2 x 5 x 10 = 25 square units.

To find the area of the unshaded part, subtract the area of the shaded triangle from the circle:

Area = 45.3416 - 25 = 20.3416

Round to two decimal places = 20.34

The answer is D. 20.34