Question

Find the complete perimeter of the sector that intercepts arc AC.

Answer 1

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