To compute the perimeter of the trapezoid with vertices A (0,0), B (5,0), C (4,3), and D (1,3), we need to find the lengths of all four sides: AB, BC, CD, and DA.
-
Calculate the lengths of the sides using the distance formula: The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
-
Calculate AB: \[ AB = \sqrt{(5 - 0)^2 + (0 - 0)^2} = \sqrt{5^2} = \sqrt{25} = 5.0 \]
-
Calculate BC: \[ BC = \sqrt{(4 - 5)^2 + (3 - 0)^2} = \sqrt{(-1)^2 + (3)^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.2 \]
-
Calculate CD: \[ CD = \sqrt{(1 - 4)^2 + (3 - 3)^2} = \sqrt{(-3)^2 + (0)^2} = \sqrt{9} = 3.0 \]
-
Calculate DA: \[ DA = \sqrt{(0 - 1)^2 + (0 - 3)^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.2 \]
-
Sum the lengths of all sides to find the perimeter: \[ \text{Perimeter} = AB + BC + CD + DA = 5.0 + 3.2 + 3.0 + 3.2 \] \[ \text{Perimeter} \approx 14.4 \]
Thus, the perimeter of the trapezoid is approximately 14.4 units.
3 answers