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The perimeter of a sector of a circle of radius 5.2cm is 16.4cm.Find the area of sector

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perimeter of a sector, p = L + 2r ---------- eqn(1)

area of a sector, a = 1/2 (Lr) ---------- eqn(2)

where r is the radius and L is the length of arc.

from eqn(2), 2a = Lr

L = 2a/r ----------- eqn(3)

substitute eqn(3) into eqn(1)

p = 2a/r + 2r

subtract 2r from both sides

p - 2r = 2a/r

multiply both sides by r

2a = r(p - 2r)

divide both sides by 2

a = r(p - 2r)/2

p = 16.4

r = 5.2

a = 5.2(16.4 - 2(5.2)) / 2

a = 31.2/2

a = 15.6 cm^{2}

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