Final answer:
The area that the circular rug will cover is approximately 38.48 m².
Step-by-step explanation:
To find the area that the circular rug will cover, we need to use the formula for the area of a circle. The formula is A = πr², where A is the area and r is the radius of the circle. In this case, the given information is the diameter of the rug, which is 7 m. The radius is half the diameter, so the radius is 7/2 = 3.5 m. Now we can find the area by substituting the radius into the formula: A = 3.1415927...(3.5 m)² = 3.1415927...×12.25 m² ≈ 38.48 m²