Given a triangle (not isosceles) ABC. Angle A = 45 °; BD-height AD = 6; DC = 3. Find Sabc

We draw a picture, consider the triangle ABD.
∠D = 90 °
∠A = 45 ° (by condition)
∠B = 180 ° – (90 ° + 45 °) = 45 °
∠A = ∠B – Therefore, the triangle is isosceles, because the angles at the base are equal.
Hence, BD = AD = 6.
Consider triangle ABC:
S = 1/2 AC * BD (height)
AC = AD + DC = 6 +3 = 9
S = 1/2 * 9 * 6 = 27
Answer: 27 (cm)