Answer:
19[tex]\pi[/tex] + 76 mm
Step-by-step explanation:
First, use the circumference formula to find the perimeter of the entire circle:
c = 2[tex]\pi[/tex]r
c = 2[tex]\pi[/tex](38)
c = 76[tex]\pi[/tex]
Divide this by 4, since the question asks for the perimeter of the quarter circle:
76[tex]\pi[/tex]/4
= 19[tex]\pi[/tex]
19[tex]\pi[/tex] is the arc length section of the perimeter. The length of the other 2 sides of the perimeter, formed by the radius, can be found by doubling 38.
38(2) = 76
Add this to 19[tex]\pi[/tex]:
19[tex]\pi[/tex] + 76
So, the expression is 19[tex]\pi[/tex] + 76 mm
