A circle is inscribed in a triangle with sides of 13 cm, 14 cm and 15 cm, the center of which is connected

| February 21, 2021 | education

A circle is inscribed in a triangle with sides of 13 cm, 14 cm and 15 cm, the center of which is connected to the vertices of the triangle. Find the area of the three triangles that have formed.

We calculate the area of the triangle using Heron’s formula:

S = √ (p * (p – a) (p – b) (p – c)), where p is the half-perimeter of the triangle, a, b and c are the sides.

p = (13 + 14 + 15) / 2 = 42/2 = 21 (cm).

S = √ (21 (21 – 13) (21 – 14) (21 – 15)) = √ (21 * 8 * 7 * 6) = √ (3 * 7 * 2 * 2 * 2 * 7 * 2 * 3 ) = 2 * 2 * 3 * 7 = 84 (cm²).

The formula for finding the area through the radius of the inscribed circle: S = p * r, hence r = S / p = 84/21 = 4 (cm).

The radius of the inscribed circle will be equal to the height of each of the three resulting triangles (the radius of the inscribed circle is perpendicular to the side of the triangle).

S1 = 1/2 * 4 * 13 = 26 (cm²).

S2 = 1/2 * 4 * 14 = 28 (cm²).

S3 = 1/2 * 4 * 15 = 30 (cm²).



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