To compute the perimeter of the trapezoid formed by the points A(0,0), B(5,0), C(4,3), and D(1,3), we first need to calculate the lengths of the sides AB, BC, CD, and DA.
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Length of AB:
\[ AB = \sqrt{(5 - 0)^2 + (0 - 0)^2} = \sqrt{5^2} = 5 \] -
Length of BC:
\[ BC = \sqrt{(4 - 5)^2 + (3 - 0)^2} = \sqrt{(-1)^2 + 3^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.2 \] -
Length of CD:
\[ CD = \sqrt{(1 - 4)^2 + (3 - 3)^2} = \sqrt{(-3)^2 + 0^2} = \sqrt{9} = 3 \] -
Length of DA:
\[ DA = \sqrt{(0 - 1)^2 + (0 - 3)^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.2 \]
Now, we can find the perimeter \(P\) of the trapezoid by adding the lengths of all sides:
\[ P = AB + BC + CD + DA \] \[ P = 5 + 3.2 + 3 + 3.2 = 14.4 \]
Rounding to the nearest tenth gives us:
\[ \text{Perimeter} = 14.4 \text{ units} \]
The correct answer is d. 14.4 units.
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