To answer, determine first the length of the arc intercepted by the angle which measures 45°.
Calculate for the circumference of the circle with the equation,
C = 2πr
where C is circumference and r is radius. Substitute the known value for r,
C = 2π(7) = 43.98
Then, multiply the obtained value by the ratio of the angle intercepted and the whole revolution.
Arc = 43.98 x (45°/360°)
Arc = 5.5
The whole perimeter of the sector includes the arc and 2 radii. Hence, the equation for the whole perimeter is,
Perimeter = Arc + 2r
Substituting the values,
Perimeter = (5.5) + 2(7)
Perimeter = 19.50
ANSWER: 19.50 units