In triangle ABC: BM-median BH-height BA = BM. Find the area of the triangle BHC if the area of the triangle ABC is 20.

Since the triangle ABM is isosceles by the condition, its area, equal to half the area of the triangle ABC, is divided by the height ВН in half.
Hence, we conclude that the area of the ВНС triangle is equal to 3/4 of the area of the ABC triangle.
Let’s find the area of the ВНС triangle, which we need to calculate according to the condition:
S (BHC) = (3/4) * 20 = 15 (exactly this value is equal to the area of the BHC triangle, which we should have found).
Answer: the area of the triangle ABC, equal to 3/4 of the area of the triangle ABC, is equal to 15.