Final answer:
The area of the sector is 50 square cm.
Step-by-step explanation:
The area of a sector is found using the formula A = (θ/2) * r^2, where θ is the central angle and r is the radius. In this case, the central angle is 2 radians and the intercepted arc is 10 cm.
We can start by finding the radius using the formula for arc length: arc length = θ * r. Substitute in the given values: 10 cm = 2 * r. Solving for r, we get r = 5 cm. Now we can calculate the area using the formula: A = (2/2) * (5 cm)^2 = 2 * 25 cm^2 = 50 cm^2. Converting to square cm, we get A = 50 square cm.