Final answer:
The area of the semicircle with a diameter of 2 mm is approximately 3.142 mm².
Step-by-step explanation:
The area of a semicircle can be found using the formula A = πr²/2, where A is the area and r is the radius. In this case, the diameter is given as 2 mm, so the radius is half of the diameter, which is 1 mm or 0.001 m.
Substituting the value of r into the formula, we get A = π(0.001 m)²/2. Simplifying, we have A = 0.000001π m².
Since the question asks for the area in square millimeters, we need to convert the units. There are 1000 millimeters in a meter, so to convert m² to mm², we multiply the value by (1000 mm/m)².
Therefore, the area of the semicircle is 0.000001π m² × (1000 mm/m)² = 0.001π mm² or approximately 3.142 mm².