Answer:
10.6149. to 4 d.p.
Step-by-step explanation:
use cosine rule to fine the length of the shaded part: sqrt(6.7^2 *2 - 2*6.7^2*cos(46degrees)) which is approx 5.24.
convert the 46degrees into radians: 46pi/180
then multiply the angle by the radius to find the arc length of the sector:
23pi/90*6.7 = arc length, which is about 5.38
23pi/90*6.7 + sqrt(2*6.7^2(1 - cos(46degrees))) which about 10.615
