To calculate the perimeter of the trapezoid with coordinates \( A(0,0) \), \( B(1,3) \), \( C(4,3) \), and \( D(5,0) \), we need to find the lengths of each side of the trapezoid \( AB \), \( BC \), \( CD \), and \( DA \).
We'll use the distance formula to find these lengths:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
-
Length of \( AB \):
- \( A(0,0) \) to \( B(1,3) \): \[ AB = \sqrt{(1 - 0)^2 + (3 - 0)^2} = \sqrt{1^2 + 3^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.2 \]
-
Length of \( BC \):
- \( B(1,3) \) to \( C(4,3) \): \[ BC = \sqrt{(4 - 1)^2 + (3 - 3)^2} = \sqrt{3^2 + 0^2} = \sqrt{9} = 3.0 \]
-
Length of \( CD \):
- \( C(4,3) \) to \( D(5,0) \): \[ CD = \sqrt{(5 - 4)^2 + (0 - 3)^2} = \sqrt{1^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.2 \]
-
Length of \( DA \):
- \( D(5,0) \) to \( A(0,0) \): \[ DA = \sqrt{(0 - 5)^2 + (0 - 0)^2} = \sqrt{(-5)^2 + 0^2} = \sqrt{25} = 5.0 \]
Now, we can calculate the total perimeter \( P \) of the trapezoid:
\[ P = AB + BC + CD + DA \] \[ P \approx 3.2 + 3.0 + 3.2 + 5.0 = 14.4 \]
Thus, the perimeter of the trapezoid is approximately 14.4 units.
1 answer