To solve this problem, we need to find the areas of both the carpet and the room and then determine how much of the room's floor the carpet will cover.
1. Calculate the Carpet Area:
- The carpet is a rectangle with a length of 11 meters and a width of 8 meters.
- The area of a rectangle is given by the formula:
[tex]\[
\text{Area} = \text{Length} \times \text{Width}
\][/tex]
- Plugging in the dimensions of the carpet:
[tex]\[
\text{Carpet Area} = 11 \, \text{m} \times 8 \, \text{m} = 88 \, \text{m}^2
\][/tex]
2. Calculate the Room Area:
- The room is a square with each side measuring 13 meters.
- The area of a square is given by the formula:
[tex]\[
\text{Area} = \text{Side}^2
\][/tex]
- Plugging in the side length of the room:
[tex]\[
\text{Room Area} = 13 \, \text{m} \times 13 \, \text{m} = 169 \, \text{m}^2
\][/tex]
3. Determine the Area Covered by the Carpet:
- Since the carpet is laid flat on the floor, we consider its own area as the area it covers on the floor.
- Therefore, the area covered by the carpet is simply its area:
[tex]\[
\text{Area Covered} = 88 \, \text{m}^2
\][/tex]
In conclusion, given that the carpet is 11 meters long and 8 meters wide, and is laid in a 13 meter by 13 meter square room, the area of the carpet is 88 square meters, the area of the room is 169 square meters, and the area covered by the carpet on the floor is 88 square meters.
