Question

find the perimeter of quadrilateral bcde. write your answer as a whole number or a decimal rounded to the nearest tenth. units

Explanation:

Step1: Identify coordinates

$B(-1,2)$, $C(2,7)$, $D(6,7)$, $E(5,1)$

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

For $BC$: $d_{BC}=\sqrt{(2 + 1)^2+(7 - 2)^2}=\sqrt{9 + 25}=\sqrt{34}\approx5.8$

Step3: For horizontal side $CD$

$x_1 = 2,y_1=7,x_2 = 6,y_2 = 7$, $d_{CD}=\vert6 - 2\vert=4$

Step4: For non - horizontal/vertical side $DE$

$d_{DE}=\sqrt{(5 - 6)^2+(1 - 7)^2}=\sqrt{1+36}=\sqrt{37}\approx6.1$

Step5: For non - horizontal/vertical side $EB$

$d_{EB}=\sqrt{(-1 - 5)^2+(2 - 1)^2}=\sqrt{36 + 1}=\sqrt{37}\approx6.1$

Step6: Calculate perimeter

$P=d_{BC}+d_{CD}+d_{DE}+d_{EB}\approx5.8 + 4+6.1+6.1 = 22.0$

Answer:

$22.0$