Question

what is the perimeter of quadrilateral stuv?
write your answer as an integer or as a decimal rounded to the nearest tenth.
perimeter = \\(\square\\) units

Explanation:

Step1: Identify coordinates of vertices

$T(-8,0), U(-4,4), V(7,-5), S(4,-9)$

Step2: Calculate length of TU

Use distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$TU=\sqrt{(-4-(-8))^2+(4-0)^2}=\sqrt{4^2+4^2}=\sqrt{32}=4\sqrt{2}\approx5.7$

Step3: Calculate length of UV

$UV=\sqrt{(7-(-4))^2+(-5-4)^2}=\sqrt{11^2+(-9)^2}=\sqrt{121+81}=\sqrt{202}\approx14.2$

Step4: Calculate length of VS

$VS=\sqrt{(4-7)^2+(-9-(-5))^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5$

Step5: Calculate length of ST

$ST=\sqrt{(-8-4)^2+(0-(-9))^2}=\sqrt{(-12)^2+9^2}=\sqrt{144+81}=\sqrt{225}=15$

Step6: Sum all side lengths

Perimeter = $TU+UV+VS+ST$

Answer:

$5.7+14.2+5+15=39.9$ units