Surprisingly, yes.
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No
Pretty close, but no.
Make it a right triangle where one side of the right triangle is half the length of the non-identical side of the isosceles, the hypotenuse of the right triangle is the length of one of the identical sides of the isosceles triangle, then use the Pythagorean theorem. a^2+b^2=c^2. Where "a" is the length of one of the identical sides, and "c" is the length of half the non-identical sides. Solve for "b" and that is your height.
There is no right triangle on the right! (Ignore the length of the hypotenuse of a right triangle.) if you have the length of the two legs (base and the upright side): (base x upright) ÷ 2 = area of the right angle triangle.
Pythagorean Theorem: a2 + b2= c2 where c is the hypotenuse of a right triangle. Hypotenuse is the side of a right triangle opposite to the right angle.