Question

what is the perimeter of polygon abcd?
a. 28 units
b. 32 units
c. 36 units
d. 44 units

Explanation:

Step1: Find length of AD

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, for $A(5,12)$ and $D(0,0)$, $AD=\sqrt{(5 - 0)^2+(12 - 0)^2}=\sqrt{25 + 144}=13$.

Step2: Find length of AB

For $A(5,12)$ and $B(9,9)$, $AB=\sqrt{(9 - 5)^2+(9 - 12)^2}=\sqrt{16 + 9}=5$.

Step3: Find length of BC

For $B(9,9)$ and $C(12,5)$, $BC=\sqrt{(12 - 9)^2+(5 - 9)^2}=\sqrt{9 + 16}=5$.

Step4: Find length of CD

For $C(12,5)$ and $D(0,0)$, $CD=\sqrt{(12 - 0)^2+(5 - 0)^2}=\sqrt{144+25}=13$.

Step5: Calculate perimeter

Perimeter $=AD + AB+BC + CD=13 + 5+5 + 13=36$.

Answer:

C. 36 units