To find the area of trapezoid DEFG with the given coordinates \( D(2, 3) \), \( E(5, 3) \), \( F(3, 1) \), and \( G(2, 1) \):
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Identify the vertices:
- D and E form one pair of vertices on the top side (with the same y-coordinate), while F and G form the bottom side.
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Identify the lengths of the bases:
- The length of base DE (top) can be calculated as the difference in x-coordinates of \( E \) and \( D \): \[ \text{Length of DE} = x_E - x_D = 5 - 2 = 3 \]
- The length of base FG (bottom) can be calculated as the difference in x-coordinates of \( G \) and \( F \): \[ \text{Length of FG} = x_F - x_G = 3 - 2 = 1 \]
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Identify the height of the trapezoid:
- The height can be calculated as the difference in the y-coordinates between the two bases (y-coordinates of DE and FG): \[ \text{Height} = y_D - y_F = 3 - 1 = 2 \]
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Use the trapezoid area formula: The area \( A \) of a trapezoid can be calculated using the formula: \[ A = \frac{1}{2} \times (b_1 + b_2) \times h \] where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height.
Plugging in our values: \[ A = \frac{1}{2} \times (3 + 1) \times 2 \] \[ A = \frac{1}{2} \times 4 \times 2 \] \[ A = \frac{1}{2} \times 8 = 4 \]
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Conclusion: The area of trapezoid DEFG is \( \boxed{4} \) square units.
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