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Find the perimeter of the shaded segment please?

Find the perimeter of the shaded segment please?-example-1

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Answer:

10.6149. to 4 d.p.

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

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