(p/(2 + sqrt(2)) | p/(2 + sqrt(2)) | (-1 + sqrt(2)) p)≈(0.292893 p | 0.292893 p | 0.414214 p) (assuming perimeter p)

(drawn with perimeter 1)

isosceles right triangle

edge lengths | (p/(2 + sqrt(2)) | p/(2 + sqrt(2)) | (-1 + sqrt(2)) p)≈(0.292893 p | 0.292893 p | 0.414214 p) area | p^2/(12 + 8 sqrt(2))≈0.0428932 p^2 interior angle sum | 180° = π rad≈3.142 rad (assuming perimeter p)