To find the area of a shape defined by points A, B, and C, you can follow these steps:
Step 1: Find the distance of the line that connects A to B and the line that connects B to C.
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Calculate the distance AB: Use the distance formula: \[ AB = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} \]
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Calculate the distance BC: Again, use the distance formula: \[ BC = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2} \]
Step 2: Multiply each distance by 2.
- Calculate the doubled distances: \[ AB_{doubled} = AB \times 2 \] \[ BC_{doubled} = BC \times 2 \]
Step 3: Add the multiplied distances.
\[ Total = AB_{doubled} + BC_{doubled} \]
Step 4: Determine whether to use the area formula relevant for the specific shape you're working with (e.g., triangle, rectangle). For example, if ABC is a triangle:
- Use the formula for the area of a triangle: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Final Answer: The final answer will depend on the specific lengths found and the calculation of the area. Make sure to state the area clearly: \[ \text{The area of the shape is } X \text{ square yards.} \] Where \(X\) will be the computed area using steps relevant to the selected shape. If the shape is not a triangle, ensure to apply the correct area formula for that shape instead.
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