BK-median of triangle ABC, AB = 12 cm, BK = 8cm, angle ABK = 30 degrees Find: Area of triangle ABC and area of triangle ABK.

The area of a triangle is found by the formula:
S = 1/2 a * h
First, we find the area ABC. For ABC, we only know AB and the height BK.
We also see an angle of 30 degrees. The side opposite to it will be equal to half of the hypotenuse.
AK = 1/2 AB
AK = 6
Now, knowing AK, you can find the whole base of AC. Since AK = KC (the median bisects the sides)
AC = AK * 2
AC = 12
We find the area.
S1 = 1/2 * 12 * 8 = 48
The area of ABK will be equal to half of the area of ABC.
S2 = 48 * 1/2 = 24.
Answer: 48; 24.