Question

A (0,0)
B (5,0)
C (4,3)
D (1,3)
Use the coordinates to compute the perimeter of the trapezoid. Round each calculation to the nearest tenth.

Answer 1

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.

1. **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:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

2. **Calculate AB:**
\[
AB = \sqrt{(5 - 0)^2 + (0 - 0)^2} = \sqrt{5^2} = \sqrt{25} = 5.0
\]

3. **Calculate BC:**
\[
BC = \sqrt{(4 - 5)^2 + (3 - 0)^2} = \sqrt{(-1)^2 + (3)^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.2
\]

4. **Calculate CD:**
\[
CD = \sqrt{(1 - 4)^2 + (3 - 3)^2} = \sqrt{(-3)^2 + (0)^2} = \sqrt{9} = 3.0
\]

5. **Calculate DA:**
\[
DA = \sqrt{(0 - 1)^2 + (0 - 3)^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.2
\]

6. **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.