Final answer:
The area of the circular gem is 19.634 square millimeters.
Step-by-step explanation:
To find the area of a circular gem, we can use the formula for the area of a circle: π * radius^2.
The diameter of the gem is given as 5 millimeters, so the radius is half of that, which is 2.5 millimeters.
Substituting this value into the formula, we get:
Area = π * (2.5)^2
= 6.25π
= 19.634 mm2
So, the area of the gem is 6.25π square millimeters.