Final answer:
The person needs to carpet an area of 300 square feet.
Step-by-step explanation:
To calculate the area of the room, we need to find the product of the length and width of the room. From the sketch provided, we can see that the length of the room is 20 feet and the width is 15 feet. Multiplying these values gives us an area of 300 square feet. Therefore, the person needs to carpet an area of 300 square feet.