The median BD is drawn in an isosceles triangle ABC (AB = BC).

The median BD is drawn in an isosceles triangle ABC (AB = BC). The area of the triangle is 36 cm ^ 2. Calculate the areas of triangles ABD and BCD.

First way.

Since ВD is the median of triangle ABC, it divides it into two equal triangles. Savd = Svsd = Savs / 2 = 36/2 = 18 cm2.

Second way.

Since AB = BC, triangle ABC is isosceles, and then ВD is also its height.

AD = СD, since ID is the median. Then Savd = AD * ВD / 2 = AC / 2 * ВD / 2 = AC * ВD / 4.

Svsd = СD * ВD / 2 = AC / 2 * ВD / 2 = AC * ВD / 4.

Svd = Svsd.

Savd + Svsd = Savd.

Savd = Svsd = Savs / 2 = 36/2 = 18 cm2.

Answer: The area of the triangles is 18 cm2.