Isabella Is building a tree fort .The base of the fort is 78 inches wide by 92 inches long. What is the area of the base in square inches? Show your work What is the area of the base in square feet? Show your work
The Correct Answer and Explanation is:
To find the area of the base of Isabella’s tree fort, we use the formula for the area of a rectangle:Area=Length×Width\text{Area} = \text{Length} \times \text{Width}Area=Length×Width
Step 1: Calculate the area in square inches
Given:
- Length = 92 inches
- Width = 78 inches
Area=92×78=7176 square inches\text{Area} = 92 \times 78 = 7176 \text{ square inches}Area=92×78=7176 square inches
So, the area of the base is 7,176 square inches.
Step 2: Convert square inches to square feet
We know that:
- 1 foot = 12 inches
- 1 square foot = 12 inches × 12 inches = 144 square inches
To convert 7,176 square inches to square feet:Area in square feet=7176144≈49.83 square feet\text{Area in square feet} = \frac{7176}{144} \approx 49.83 \text{ square feet}Area in square feet=1447176≈49.83 square feet
So, the area of the base is approximately 49.83 square feet.
Explanation:
To solve this problem, we begin with understanding that a rectangle’s area is found by multiplying its length and width. Both of these values are given in inches. Isabella’s tree fort base measures 78 inches wide and 92 inches long. By multiplying these two dimensions, we calculate how much flat space the base covers. This calculation gives:92×78=7176 square inches92 \times 78 = 7176 \text{ square inches}92×78=7176 square inches
This tells us the area in terms of square inches. However, sometimes it is more useful to express area in square feet, especially when building or comparing to larger spaces.
Since one foot is equal to twelve inches, one square foot equals twelve inches times twelve inches, which is 144 square inches. To convert from square inches to square feet, we divide the total number of square inches by 144:7176÷144≈49.83 square feet7176 \div 144 \approx 49.83 \text{ square feet}7176÷144≈49.83 square feet
This result shows that the base of the tree fort is just under 50 square feet. Using square feet makes it easier to visualize the size, especially when thinking about how much space someone would have inside the fort. This kind of conversion is also important when purchasing materials like flooring or estimating construction costs, as those are typically measured in square feet.
