Question

question 1 of 5 select the correct answer. what is the best approximation for the perimeter of the pentagon abcde?

Explanation:

Step1: Find distance formula

The distance 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: Find length of EA

Let $E(0,0)$ and $A(2,4)$. Then $EA=\sqrt{(2 - 0)^2+(4 - 0)^2}=\sqrt{4 + 16}=\sqrt{20}\approx4.47$.

Step3: Find length of AB

Let $A(2,4)$ and $B(6,3)$. Then $AB=\sqrt{(6 - 2)^2+(3 - 4)^2}=\sqrt{16 + 1}=\sqrt{17}\approx4.12$.

Step4: Find length of BC

Let $B(6,3)$ and $C(8,0)$. Then $BC=\sqrt{(8 - 6)^2+(0 - 3)^2}=\sqrt{4+9}=\sqrt{13}\approx3.61$.

Step5: Find length of CD

Let $C(8,0)$ and $D(2,- 3)$. Then $CD=\sqrt{(2 - 8)^2+(-3 - 0)^2}=\sqrt{36 + 9}=\sqrt{45}\approx6.71$.

Step6: Find length of DE

Let $D(2,-3)$ and $E(0,0)$. Then $DE=\sqrt{(0 - 2)^2+(0+3)^2}=\sqrt{4 + 9}=\sqrt{13}\approx3.61$.

Step7: Calculate perimeter

Perimeter $P=EA + AB+BC + CD+DE\approx4.47+4.12+3.61+6.71+3.61 = 22.52\approx22$.

Answer:

22 units