Question

find the perimeter of the quadrilateral. round to the nearest tenth if necessary. note: these figures are parallelograms.
a. 807
b. 17.8
c. 18.9
d. 24.3

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length of one - side

Let's find the distance between $(-1.7,1)$ and $(3,1)$. Here $x_1=-1.7,y_1 = 1,x_2=3,y_2 = 1$. Then $d_1=\sqrt{(3+1.7)^2+(1 - 1)^2}=\sqrt{(4.7)^2+0^2}=4.7$.

Step3: Calculate length of adjacent - side

Let's find the distance between $(-1.7,1)$ and $(-3,-3)$. Here $x_1=-1.7,y_1 = 1,x_2=-3,y_2=-3$. Then $d_2=\sqrt{(-3 + 1.7)^2+(-3 - 1)^2}=\sqrt{(-1.3)^2+(-4)^2}=\sqrt{1.69 + 16}=\sqrt{17.69}\approx4.2$.

Step4: Calculate perimeter of parallelogram

Since opposite sides of a parallelogram are equal, the perimeter $P = 2(d_1 + d_2)$. Substitute $d_1 = 4.7$ and $d_2=4.2$ into the formula. $P=2(4.7+4.2)=2\times8.9 = 17.8$.

Answer:

b. 17.8