Question

determine the perimeter of the given figure on the coordinate plane. round your answer to the nearest hundredth, if necessary. trapezoid efgh > enter the answer in the space provided. use numbers instead of words. units

Explanation:

Step1: Identify coordinates

Assume \(E(-6,-8)\), \(F(-4, - 4)\), \(G(0,-4)\), \(H(0,-8)\)

Step2: Use distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for non - horizontal/vertical sides

For side \(EF\): \(x_1=-6,y_1 = - 8,x_2=-4,y_2=-4\)
\[

$$\begin{align*} d_{EF}&=\sqrt{(-4+6)^2+(-4 + 8)^2}\\ &=\sqrt{2^2+4^2}\\ &=\sqrt{4 + 16}\\ &=\sqrt{20}=2\sqrt{5}\approx4.47 \end{align*}$$

\]

Step3: Calculate length of horizontal side \(EH\)

\(x_1=-6,x_2 = 0,y_1=y_2=-8\), \(d_{EH}=\vert0+6\vert = 6\)

Step4: Calculate length of vertical side \(GH\)

\(x_1=x_2 = 0,y_1=-4,y_2=-8\), \(d_{GH}=\vert-8 + 4\vert=4\)

Step5: Calculate length of side \(FG\)

\(x_1=-4,x_2 = 0,y_1=y_2=-4\), \(d_{FG}=\vert0 + 4\vert=4\)

Step6: Calculate perimeter \(P\)

\(P=d_{EF}+d_{EH}+d_{GH}+d_{FG}\approx4.47+6 + 4+4=18.47\)

Answer:

\(18.47\)