To find the area of the actual bridge deck in square feet given the dimensions of the scaled drawing and the scale ratio, follow these steps:
1. Understand the Scale Ratio:
The scale ratio is 40.1. This means that each inch in the scale drawing represents 40.1 inches in reality.
2. Scaled Dimensions:
The dimensions of the scaled bridge deck are provided as:
- Length: 24 inches
- Width: [tex]\( 4 \frac{4}{5} \)[/tex] inches, which can be converted to a decimal as [tex]\( 4.8 \)[/tex] inches (since [tex]\( 4 + \frac{4}{5} = 4 + 0.8 = 4.8 \)[/tex]).
3. Convert Scaled Dimensions to Actual Dimensions:
Multiply each dimension by the scale factor to get the actual dimensions:
- Actual Length = 24 inches 40.1 = 962.4 inches
- Actual Width = 4.8 inches 40.1 = 192.48 inches
4. Calculate the Area in Square Inches:
- Actual Area (in square inches) = Actual Length Actual Width
- [tex]\( 962.4\)[/tex] inches [tex]\( 192.48 \)[/tex] inches = 185,242.752 square inches
5. Convert the Area to Square Feet:
- Since there are 144 square inches in a square foot, we need to divide the area in square inches by 144.
- [tex]\( \frac{185,242.752 \text{ square inches}}{144 \text{ square inches per square foot}} = 1,286.408 \text{ square feet} \)[/tex]
Thus, the area of the actual bridge deck is approximately 1,280 square feet. The correct answer is:
- 1,280 square feet
Therefore, the answer is:
1,280 square feet
