Answer:
14.283 km
Step-by-step explanation:
The circumference of the entire circle is given by ...
C = 2πr
so the length of the curved perimeter of the quarter-circle is 1/4 of that:
1/4C = (1/4)2πr = (π/2)r
The straight sides of the quarter-circle are both equal to the radius, so the total of all sides of the quarter-circle is ...
P = 2r +(π/2)r = (2+π/2)r
P ≈ (3.570796)(4 km) ≈ 14.283 km
The quarter-circle's perimeter is about 14.283 km.
