find the area of the door 80 inches by 36 inches and convert to square feet
The Correct Answer and Explanation is:
t’s calculate the area of a door that is 80 inches tall and 36 inches wide.
Step 1: Find the area in square inches
The area of a rectangle is found by multiplying its length by its width.Area=Length×Width\text{Area} = \text{Length} \times \text{Width}Area=Length×Width
Given:
- Length = 80 inches
- Width = 36 inches
Thus:Area=80×36=2,880 square inches\text{Area} = 80 \times 36 = 2,880 \, \text{square inches}Area=80×36=2,880square inches
Step 2: Convert square inches to square feet
There are 12 inches in one foot. Therefore, one square foot equals:12×12=144 square inches12 \times 12 = 144 \, \text{square inches}12×12=144square inches
To convert from square inches to square feet, divide the area in square inches by 144:Area in square feet=2,880144=20 square feet\text{Area in square feet} = \frac{2,880}{144} = 20 \, \text{square feet}Area in square feet=1442,880=20square feet
Final Answer:
The area of the door is 20 square feet.
Detailed Explanation
The problem involves finding the area of a door using basic principles of geometry and unit conversion. The shape of the door is rectangular, so its area is calculated by multiplying its height by its width. Both dimensions are initially provided in inches. After calculating the area in square inches, it is necessary to convert the measurement into square feet since area is often more practical to express in square feet for larger objects like doors or rooms.
The conversion from inches to feet must account for the fact that the area unit is squared. Since there are 12 inches in one foot, there are 12 × 12, or 144, square inches in one square foot. Dividing the area in square inches by 144 yields the area in square feet. This step is crucial because failing to square the conversion factor would result in an incorrect calculation.
This method applies to any rectangular surface where dimensions are given in inches but the area is needed in square feet. Mastery of this conversion ensures accurate results in fields such as construction, interior design, and architecture.
