Question

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

Answer 1

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.

1. **Calculate the length of AB:**
\[
AB = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} = \sqrt{(5 - 0)^2 + (0 - 0)^2} = \sqrt{5^2} = 5
\]

2. **Calculate the length of BC:**
\[
BC = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2} = \sqrt{(4 - 5)^2 + (3 - 0)^2} = \sqrt{(-1)^2 + 3^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.2
\]

3. **Calculate the length of CD:**
\[
CD = \sqrt{(x_D - x_C)^2 + (y_D - y_C)^2} = \sqrt{(1 - 4)^2 + (3 - 3)^2} = \sqrt{(-3)^2 + 0^2} = \sqrt{9} = 3
\]

4. **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).