To find the area of a semicircle with a given radius, we follow these steps:
1. Calculate the area of the full circle.
The formula for the area of a circle is given by:
[tex]\[
\text{Area of a full circle} = \pi r^2
\][/tex]
where [tex]\( r \)[/tex] is the radius.
Given:
[tex]\[
r = 19 \text{ mm}
\][/tex]
and
[tex]\[
\pi \approx 3.14
\][/tex]
Substituting the values, we get:
[tex]\[
\text{Area of the full circle} = 3.14 \times (19)^2
\][/tex]
2. Square the radius.
[tex]\[
19^2 = 361
\][/tex]
3. Multiply by [tex]\(\pi\)[/tex].
[tex]\[
\text{Area of the full circle} = 3.14 \times 361 = 1133.54 \text{ square millimeters}
\][/tex]
4. Calculate the area of the semicircle.
Since a semicircle is half of a full circle, its area is half of the area of the full circle.
[tex]\[
\text{Area of the semicircle} = \frac{1133.54}{2} = 566.77 \text{ square millimeters}
\][/tex]
Therefore, the area of the semicircle with a radius of 19 millimeters, rounded to the nearest hundredth, is [tex]\( 566.77 \)[/tex] square millimeters.
