Find the area of the triangle ACM. 1 side 4 cm, 2 side 5 cm, 3 side 7 cm.

Given:
AC = 4 cm;

CM = 5 cm;

MA = 7 cm;
S =? cm².

To calculate the area of a triangle with known lengths of three sides, we use Heron’s formula S = √p (p – a) * (p – b) * (p – c).

Find the half-perimeter of the triangle by the formula p = (a + b + c): 2;

1) p = (4 + 5 + 7): 2 = 16: 2 = 8 (cm).

2) p – a = 8 – 4 = 4;

3) p – b = 8 – 5 = 3;

4) p – c = 8 – 7 = 1;

5) S = √ (8 * 4 * 3 * 1) = √96 = 9.8 (cm²).
Answer: 9.8 cm² is the area of the ACM triangle.