Question

Use the coordinates to compute the perimeter of the trapezoid. Round each calculation to the nearest tenth. (1 point) Responses 16.3 units 16.3 units 12.3 units 12.3 units 13.8 units 13.8 units 14.4 units the coords are (0,0) (1,3) (4,3) (5,0)

Answer 1

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:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

1. **Length of \( AB \)**:
- \( A(0,0) \) to \( B(1,3) \):
\[
AB = \sqrt{(1 - 0)^2 + (3 - 0)^2} = \sqrt{1^2 + 3^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.2
\]

2. **Length of \( BC \)**:
- \( B(1,3) \) to \( C(4,3) \):
\[
BC = \sqrt{(4 - 1)^2 + (3 - 3)^2} = \sqrt{3^2 + 0^2} = \sqrt{9} = 3.0
\]

3. **Length of \( CD \)**:
- \( C(4,3) \) to \( D(5,0) \):
\[
CD = \sqrt{(5 - 4)^2 + (0 - 3)^2} = \sqrt{1^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.2
\]

4. **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**.