Question

a rancher has a field in the shape of the polygon shown. the rancher plans to keep one sheep in the field for every 2,000 m². based on this plan, how many sheep can the rancher keep in the field? show your work.

Explanation:

Step1: Divide the polygon into a rectangle and a right - triangle

The polygon can be divided into a rectangle with sides 200m and 200m and a right - triangle with base $200 - 120=80$m and height $200 - 100 = 100$m.

Step2: Calculate the area of the rectangle

The area of a rectangle $A_{rect}=l\times w$, where $l = 200$m and $w = 200$m. So $A_{rect}=200\times200=40000$m².

Step3: Calculate the area of the right - triangle

The area of a right - triangle $A_{tri}=\frac{1}{2}\times b\times h$, where $b = 80$m and $h = 100$m. So $A_{tri}=\frac{1}{2}\times80\times100 = 4000$m².

Step4: Calculate the total area of the polygon

$A = A_{rect}+A_{tri}=40000 + 4000=44000$m².

Step5: Calculate the number of sheep

The number of sheep $n=\frac{A}{2000}$, where $A = 44000$m². So $n=\frac{44000}{2000}=22$.

Answer:

22