To calculate the perimeter of the trapezoid defined by the coordinates A(0,0), B(5,0), C(4,3), and D(1,3), we need to calculate the lengths of each side: AB, BC, CD, and DA.
-
Calculate the length of AB: \[ AB = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} = \sqrt{(5 - 0)^2 + (0 - 0)^2} = \sqrt{5^2} = 5 \]
-
Calculate the length of BC: \[ BC = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2} = \sqrt{(4 - 5)^2 + (3 - 0)^2} = \sqrt{(-1)^2 + 3^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.2 \]
-
Calculate the length of CD: \[ CD = \sqrt{(x_D - x_C)^2 + (y_D - y_C)^2} = \sqrt{(1 - 4)^2 + (3 - 3)^2} = \sqrt{(-3)^2 + 0^2} = \sqrt{9} = 3 \]
-
Calculate the length of DA: \[ DA = \sqrt{(x_A - x_D)^2 + (y_A - y_D)^2} = \sqrt{(0 - 1)^2 + (0 - 3)^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.2 \]
Now we can sum up all the lengths to find the perimeter of the trapezoid: \[ \text{Perimeter} = AB + BC + CD + DA = 5 + 3.2 + 3 + 3.2 \] Calculating this gives: \[ \text{Perimeter} = 5 + 3.2 + 3 + 3.2 = 14.4 \]
Thus, the perimeter of the trapezoid is approximately 14.4 (rounded to the nearest tenth).