Given:
- Two sides of the triangle: 18 cm and 10 cm
- Perimeter of the triangle: 42 cm

Finding the third side:
To find the third side of the triangle, we can subtract the sum of the two given sides from the perimeter of the triangle:
Third side = Perimeter - (Side 1 + Side 2)
Third side = 42 cm - (18 cm + 10 cm)
Third side = 42 cm - 28 cm
Third side = 14 cm

Calculating the semi-perimeter:
To find the semi-perimeter of the triangle, we can use the formula:
Semi-perimeter = Perimeter / 2
Semi-perimeter = 42 cm / 2
Semi-perimeter = 21 cm

Using Heron's formula to find the area:
Now, we can use Heron's formula to calculate the area of the triangle:
Area = √[s(s - a)(s - b)(s - c)]
where a, b, and c are the sides of the triangle, and s is the semi-perimeter.
Substitute the values into the formula:
Area = √[21(21 - 18)(21 - 10)(21 - 14)]
Area = √[21(3)(11)(7)]
Area = √[21(231)]
Area = √4851
Area ≈ 69.68 cm²

Conclusion:
Therefore, the area of the triangle with sides of 18 cm, 10 cm, and 14 cm, and a perimeter of 42 cm is approximately 69.68 cm².