Question

find the perimeter of the trapezoid with these vertices.
(5, 2), (5, -3), (2, 2), (-4, -3)
give an exact answer (not a decimal approximation).
simplify your answer as much as possible.
scratch area (not part of answer)

Explanation:

Step1: Calculate the length of each side using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ or for vertical/horizontal lines.

• For the vertical side between $(5,2)$ and $(5, - 3)$: $|2-(-3)|=5$.
• For the horizontal side between $(5,2)$ and $(2,2)$: $|5 - 2|=3$.
• For the side between $(2,2)$ and $(-4,-3)$:

$$\begin{align*} d&=\sqrt{(-4 - 2)^2+(-3 - 2)^2}\\ &=\sqrt{(-6)^2+(-5)^2}\\ &=\sqrt{36 + 25}\\ &=\sqrt{61} \end{align*}$$

• For the side between $(-4,-3)$ and $(5,-3)$: $|5-(-4)| = 9$.

Step2: Sum up the lengths of all sides.

The perimeter $P=5 + 3+\sqrt{61}+9$.

Answer:

$17+\sqrt{61}$