Certainly! Let's solve this step-by-step.
1. Convert the front area to inches:
- Convert yards to inches:
- [tex]\(140 \text{ yards} = 140 \times 3 \times 12 \text{ inches} = 5040 \text{ inches}\)[/tex]
- Convert feet to inches:
- [tex]\(2 \text{ feet} = 2 \times 12 \text{ inches} = 24 \text{ inches}\)[/tex]
- Add the existing inches:
- [tex]\(9 \text{ inches}\)[/tex]
Adding these together:
[tex]\[
5040 \text{ inches} (from yards) + 24 \text{ inches} (from feet) + 9 \text{ inches} = 5073 \text{ inches}
\][/tex]
2. Convert the back area to inches:
- Convert yards to inches:
- [tex]\(170 \text{ yards} = 170 \times 3 \times 12 \text{ inches} = 6120 \text{ inches}\)[/tex]
- Convert feet to inches:
- [tex]\(1 \text{ foot} = 1 \times 12 \text{ inches} = 12 \text{ inches}\)[/tex]
- Add the existing inches:
- [tex]\(6 \text{ inches}\)[/tex]
Adding these together:
[tex]\[
6120 \text{ inches} (from yards) + 12 \text{ inches} (from feet) + 6 \text{ inches} = 6138 \text{ inches}
\][/tex]
3. Find the total area in inches:
[tex]\[
5073 \text{ inches} + 6138 \text{ inches} = 11211 \text{ inches}
\][/tex]
4. Convert the total inches back to yards, feet, and inches:
- Convert inches to yards:
- One yard is [tex]\(3 \times 12 = 36\)[/tex] inches.
[tex]\[
\text{Yards} = \left\lfloor \frac{11211 \text{ inches}}{36} \right\rfloor = 311 \text{ yards}
\][/tex]
- Compute remaining inches after converting to yards:
[tex]\[
11211 \text{ inches} \mod 36 = 15 \text{ inches}
\][/tex]
- Convert remaining inches to feet:
[tex]\[
\text{Feet} = \left\lfloor \frac{15 \text{ inches}}{12} \right\rfloor = 1 \text{ foot}
\][/tex]
- Compute remaining inches after converting to feet:
[tex]\[
15 \text{ inches} \mod 12 = 3 \text{ inches}
\][/tex]
Hence, the total area is:
[tex]\[
311 \text{ yards}, 1 \text{ foot}, and 3 \text{ inches}
\][/tex]
So, the total area of the community center is 311 yards 1 foot 3 inches.
