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

| September 5, 2021 | education

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

The ABC triangle is isosceles, which means that the medians ВK, CP and the median from the vertex A intersect at one point M, which divides each of them in a ratio of 2: 1, counting from the vertex. We know the part of the median from the vertex A (which will also be the height of the isosceles triangle) – it is 4 cm, so the remaining part is 2 cm (2: 1 = 4: 2). It turns out the height from the top A is 6 cm (4 + 2 = 6 cm).

We look for the area of ​​an isosceles triangle ABC by the formula: S = 1/2 * h * c, where h is the height lowered to the base of the triangle (6 cm), and c is the base of the triangle (9 cm).

Substitute the values ​​into the formula: S = 1/2 * 6 * 9 = 27 cm2.



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