Question

determine the perimeter of the given figure on the coordinate plane. round your answer to the nearest hundredth, if necessary. trapezoid abcd

Explanation:

Step1: Identify side - lengths

By counting grid - squares on the coordinate plane:

• $AB$: Horizontal side, from $x=-8$ to $x = - 6$, so $AB=\vert-6-(-8)\vert = 2$.
• $BC$: Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $B(-6,8)$ and $C(-2,4)$, $x_1=-6,y_1 = 8,x_2=-2,y_2 = 4$. Then $BC=\sqrt{(-2+6)^2+(4 - 8)^2}=\sqrt{4^2+( - 4)^2}=\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2}\approx5.66$.
• $CD$: Horizontal side, from $x=-2$ to $x=-8$, so $CD=\vert-8-(-2)\vert = 6$.
• $DA$: Vertical side, from $y = 4$ to $y = 8$, so $DA=\vert8 - 4\vert=4$.

Step2: Calculate perimeter

The perimeter $P$ of trapezoid $ABCD$ is $P=AB + BC+CD + DA$.
$P=2+5.66+6 + 4=17.66$.

Answer:

$17.66$