To find the area of a triangle with two sides given and the perimeter, we can use Heron's formula. Heron's formula states that the area of a triangle can be calculated using the lengths of its sides and the perimeter.

Heron's Formula:
Let's denote the lengths of the sides of the triangle as a, b, and c, and the semiperimeter as s (half of the perimeter).
The area of the triangle can be calculated using the following formula:

Area = sqrt(s(s-a)(s-b)(s-c))

where s = (a + b + c)/2

Now let's solve the problem step by step.

Step 1: Identify the given information:
- Two sides of the triangle are 18cm and 10cm
- The perimeter of the triangle is 42cm

Step 2: Calculate the semiperimeter (s):
Given that the perimeter is the sum of all three sides, we can write the equation as:
42 = 18 + 10 + c
42 = 28 + c
c = 42 - 28
c = 14

The semiperimeter (s) is half of the perimeter, so:
s = (18 + 10 + 14)/2
s = 21

Step 3: Calculate the area using Heron's formula:
Using the formula:
Area = sqrt(s(s-a)(s-b)(s-c))

Area = sqrt(21(21-18)(21-10)(21-14))
Area = sqrt(21 * 3 * 11 * 7)
Area = sqrt(539)
Area ≈ 23.21 cm²

Therefore, the area of the triangle with sides measuring 18cm, 10cm, and 14cm (perimeter = 42cm) is approximately 23.21 cm².