AB = 16 cm CD = 12 cm Angle ABD = 30 degrees Find the area of triangle ABC.

Let’s find out from the beginning what the triangle is.

BD is the median, which means that AD = DC.

CD = 12 cm, so AD = 12 cm.

AC = AD + DC = 12 + 12 = 24 cm.

The ABC triangle is isosceles, which means that the median is the BD height.

Let’s find the angle ВСD.

It follows that the triangle ABD is rectangular, which means that the angle ABD = BCD = 30 degrees.

Let’s find the angle ABC.

ABC = ABD + BCD = 30 + 30 = 60 degrees.

Let’s find the side of the BC.

Since triangle ABC is isosceles, side AB = side BC, that is, BC = 16 cm.

Let’s find the area of ​​the triangle ABC.

sin 60 degrees = √3 / 2

S = 1/2 * AB * BC * sin of angle ABC = 1/2 * 16 * 16 * √3 / 2 = 64√3 = 108.8 cm2.

Answer: the area of ​​the triangle ABC is 108.8 cm2.