The medians of the triangle are 3 cm, 4 cm, 5 cm. Find the area of the triangle.

| January 30, 2021 | education

The median of a triangle is the line segment that connects the midpoints of the two sides of the triangle and is parallel to the third side. The median of a triangle is half the parallel side. This means that the sides of the triangle are 2 times larger than the average of the extra triangle.

3 * 2 = 6 (cm) – the first side of the triangle;

4 * 2 = 8 (cm) – the second side of the triangle;

5 * 2 = 10 (cm) – the third side of the triangle.

We find the area of ​​the triangle using Heron’s formula. S = √ (p (p – a) (p – b) (p – c)), where a, b, c are the sides of the triangle, p is the semiperimeter. p = (a + b + c) / 2.

p = (6 + 8 + 10) / 2 = 24/2 = 12 (cm);

S = √ (12 (12 – 6) (12 – 8) (12 – 10)) = √ (12 * 6 * 4 * 2) = √ (24 * 24) = 24 (cm ^ 2).

Answer. 24 cm ^ 2.



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