To find the perimeter of a semicircle with a radius of 7 cm, we need to follow these steps:
1. Understand the components of the perimeter:
- The perimeter of a semicircle is made up of half the circumference of the full circle plus the diameter of the circle.
2. Calculate the circumference of the full circle:
- The formula for the circumference of a full circle is [tex]\(2 \pi r\)[/tex], where [tex]\(r\)[/tex] is the radius.
For a circle with radius 7 cm:
[tex]\[
\text{Circumference} = 2 \pi \times 7 = 14 \pi
\][/tex]
3. Calculate half of the circumference:
- Since we are dealing with a semicircle, we only need half of the full circumference.
[tex]\[
\text{Half the circumference} = \frac{14 \pi}{2} = 7 \pi
\][/tex]
4. Calculate the diameter of the circle:
- The diameter ([tex]\(d\)[/tex]) is twice the radius ([tex]\(r\)[/tex]).
For a circle with radius 7 cm:
[tex]\[
\text{Diameter} = 2 \times 7 = 14 \text{ cm}
\][/tex]
5. Add the half circumference and the diameter to get the perimeter of the semicircle:
- The total perimeter of the semicircle is the sum of the half circumference and the diameter.
[tex]\[
\text{Perimeter} = 7 \pi + 14
\][/tex]
Therefore, the perimeter of the semicircle with a radius of 7 cm, in terms of [tex]\(\pi\)[/tex], is:
[tex]\[
\boxed{7 \pi + 14 \text{ cm}}
\][/tex]
