In an isosceles triangle with base AC, the median BM is drawn, equal to 6. Find the area of the triangle

In an isosceles triangle with base AC, the median BM is drawn, equal to 6. Find the area of the triangle if the lateral side is 10.

1. Considering that the median BM divides the base of the AC into two equal segments, CM and AM are equal.

2. Triangle MBC is rectangular, since the median BM in an isosceles triangle is also the height.

3. Using the formula of the Pythagorean theorem, we calculate the length of the segments CM and AM:

CM = AM = √BC ^ 2 – BM ^ 2 = √10 ^ 2 – 6 ^ 2 = √100 – 36 = √64 = 8 cm.

4. AC = CM + AM = 8 + 8 = 16 cm.

5. The area of the triangle ABC = AC / 2 x BM = (16: 2) x 6 = 48 cm ^ 2.

Answer: the area of the triangle ABC is 48 cm ^ 2.