You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.
system
<image>Compute the area, error in the area, and the standard error of the area for Fig. 1 using the following data:a = 50.30 $\pm $ 0.01 m,b = 82.65 $\pm$ 0.03 m,r = 9.50 $\pm $ 0.02 m.The measurements were made with 30 m tape standardized at 30° C and the field temperature during the measurements was 50° C. Take coefficient of linear expansion = 1.15 * $10^{-5}$ per ° C.<image 1>
A. 5136.82 $m_{2}$, 2.43 $m_{2}$, $\pm$ 2.34 $m_{2}$
B. 5134.82 $m_{2}$, 2.43 $m_{2}$, $\pm$ 2.34 $m_{2}$
C. 5138.82 $m_{2}$, 2.43 $m_{2}$, $\pm$ 2.34 $m_{2}$
D. 5132.82 $m_{2}$, 2.43 $m_{2}$, $\pm$ 2.34 $m_{2}$

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
user
C
Compute the area, error in the area, and the standard error of the area for Fig. 1 using the following data:a = 50.30 $\pm $ 0.01 m,b = 82.65 $\pm$ 0.03 m,r = 9.50 $\pm $ 0.02 m.The measurements were made with 30 m tape standardized at 30° C and the field temperature during the measurements was 50° C. Take coefficient of linear expansion = 1.15 * $10^{-5}$ per ° C.<image 1>
A. 5136.82 $m_{2}$, 2.43 $m_{2}$, $\pm$ 2.34 $m_{2}$
B. 5134.82 $m_{2}$, 2.43 $m_{2}$, $\pm$ 2.34 $m_{2}$
C. 5138.82 $m_{2}$, 2.43 $m_{2}$, $\pm$ 2.34 $m_{2}$
D. 5132.82 $m_{2}$, 2.43 $m_{2}$, $\pm$ 2.34 $m_{2}$

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
val