Question

A (0,0)
B (5,0)
C (4,3)
D (1,3)


Using the coordinates to compute the perimeter of the trapezoid. Round each calculation to the nearest tenth

a. 12.3 units
b. 16.3 units
c. 13.8 units
d. 14.4 units

Answer 1

To compute the perimeter of the trapezoid formed by the points A(0,0), B(5,0), C(4,3), and D(1,3), we first need to calculate the lengths of the sides AB, BC, CD, and DA.

1. **Length of AB**:
\[
AB = \sqrt{(5 - 0)^2 + (0 - 0)^2} = \sqrt{5^2} = 5
\]

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

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

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

Now, we can find the perimeter \(P\) of the trapezoid by adding the lengths of all sides:

\[
P = AB + BC + CD + DA
\]
\[
P = 5 + 3.2 + 3 + 3.2 = 14.4
\]

Rounding to the nearest tenth gives us:

\[
\text{Perimeter} = 14.4 \text{ units}
\]

The correct answer is **d. 14.4 units**.