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Suppose the base of the triangle is of length x cm and the equal sides are of length y cm.

The base angles sum to 60 degrees so each is 30 degrees and the apex angle is 180-60 = 120 degrees.

Then area = 132.61014 = 0.5*y2*sin(120)

So that y2 = 132.61014/[0.5*sin(120)] = 306.25

and therefore, y = 17.5 cm.

Then, by the sine rule, x/sin(120) = y/sin(30)

So x = y*sin(120)/sin(30) = 30.31 cm

And therefore, perimeter = x + 2*y = 65.31 cm.

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Q: What is the perimeter of an isosceles triangle whose base angles add up to 60 degrees and has an area of 132.61014 square cm showing work?
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