In an isosceles triangle ABC AB = AC, the medians BK and CP intersect at the point M

In an isosceles triangle ABC AB = AC, the medians BK and CP intersect at the point M, AM = 4 cm, BC = 9 cm. what is the area of triangle ABC

Let us construct the median AH of the isosceles triangle ABC.

All three medians intersect at one point M and are divided in it in a ratio of 2/1 starting from the top.

Then AM / HM = 2/1.

HM = AM / 2 = 4/2 = 2 cm.

Then the median AH = AM + HM = 4 + 2 = 6 cm.

The median AH is drawn to the base of the BC of an isosceles triangle, then AH is also the height of the ABC triangle.

Determine the area of the triangle ABC.

Sас = ВС * АН / 2 = 9 * 6/2 = 27 cm2.

Answer: The area of triangle ABC is 27 cm2.