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You will need to find the surface area of each face and add them together.
If it's a right triangle, use pythagorean's theorem (a2+b2=c2) to solve it. = If it's an oblique triangle, use the law of sines or cosines (see related link)
Drop a perpendicular..... then using Pythagoras theorem, find h in terms of x (x=base - remaining length) for both the triangles which are on right & left side to the perpendicular height.... both answers are in terms of x, now compare h to find x, then find h ultimately.
Let the sides be a, b, c Area = sq rt [s(s-a)(s-b)(s-c)] where s= 1/2 (a+b+c)