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Difficulty: MediumPerimeter and Area of 2D Figures

A rectangular floor is 1818 feet long and 1212 feet wide. A square rug with a side length of 99 feet is placed on the floor. What is the area of the floor that is NOT covered by the rug, in square feet?

  1. A
    180180
  2. B
    2424
  3. 135135Answer
  4. D
    297297

Answer

The area of the floor not covered by the rug is 135135 square feet.
The correct answer is found by calculating the total area of the floor (18×12=21618 \times 12 = 216 sq ft) and subtracting the area of the square rug (9×9=819 \times 9 = 81 sq ft). This gives an uncovered area of 216−81=135216 - 81 = 135 square feet.

Step-by-Step Solution

1
Calculate the total area of the rectangular floor.
Area of floor=18×12=216 square feet\text{Area of floor} = 18 \times 12 = 216 \text{ square feet}
The area of a rectangle is found by multiplying its length by its width.
2
Calculate the area of the square rug.
Area of rug=9×9=81 square feet\text{Area of rug} = 9 \times 9 = 81 \text{ square feet}
The area of a square is found by squaring its side length.
3
Subtract the area of the rug from the total area of the floor.
216−81=135 square feet216 - 81 = 135 \text{ square feet}
The uncovered area is the difference between the total floor area and the area covered by the rug.

Key Concept

Calculating and subtracting areas of 2D figures
Estimated Time:1m 0s
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Topics

Perimeter and Area of 2D Figures

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