Answer:
The perimeter of the stained glass semi-circle is 3π feet.
Explanation:
The perimeter of a semi-circle is half of the circumference of the full circle with the same diameter.
The circumference of a circle with diameter 3 feet is:
C = πd = π(3) = 3π feet
Therefore, the circumference of the full circle is 3π feet, and the circumference of the semi-circle is half of that:
C(semi-circle) = 1/2(3π) = 3/2π feet
However, the stained glass semi-circle has a curved edge, so we need to add the length of that edge to the perimeter. The curved edge of a semi-circle is half of the circumference of the full circle, or:
C(curved edge) = 1/2(2πr) = πr, where r is the radius of the circle
Since the diameter of the circle is 3 feet, the radius is half of that:
r = d/2 = 3/2 feet
So the curved edge of the stained glass semi-circle is:
C(curved edge) = π(3/2) = 3/2π feet
Adding this to the straight edge perimeter, we get:
Perimeter = C(semi-circle) + C(curved edge)
= (3/2π) + (3/2π)
= 3π feet
Therefore, the perimeter of the stained glass semi-circle is 3π feet.