The radius of the circle inscribed in the triangle is 4.5 cm and the lengths of the sides of the triangle

The radius of the circle inscribed in the triangle is 4.5 cm and the lengths of the sides of the triangle are 15 cm 15 cm and 18 cm, calculate the area of the triangle.

First of all, it should be noted that the task contains redundant information for calculating the area S of the triangle. We will use this information; calculate S in two ways and check the correspondence of the data to each other.
First, we calculate the semiperimeter p of the given triangle p = (a + b + c) / 2, where a, b and c are the lengths of the sides of the triangle, that is, a = 15 cm, b = 15 cm and c = 18 cm.We have: p = (15 cm + 15 cm + 18 cm) / 2 = (48 cm) / 2 = 24 cm.
First way. Along the radius r = 4.5 cm of the inscribed circle in the triangle and the semi-perimeter p = 24 cm, according to the formula S = r * p. We have: S = (4.5 cm) * (24 cm) = 108 cm².
Second way. On three sides, a = 15 cm, b = 15 cm and c = 18 cm, according to Heron’s formula S = √ [p * (p – a) * (p – b) * (p – c)]. We have: S = √ [(24 cm) * (24 cm – 15 cm) * (24 cm – 15 cm) * (24 cm – 18 cm)] = √ (24 * 9 * 9 * 6) cm² = 108 cm² …
Calculations show that the data is consistent.