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 shapes

Divide the polygon into a rectangle and a trapezoid. The rectangle has dimensions $200$m by $200$m, and the trapezoid has bases $100$m and $200$m and height $80$m.

Step2: Calculate rectangle area

The area formula for a rectangle is $A = l\times w$. For the rectangle with $l = 200$m and $w=200$m, $A_{rectangle}=200\times200 = 40000$ $m^{2}$.

Step3: Calculate trapezoid area

The area formula for a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$, where $b_1 = 100$m, $b_2 = 200$m and $h = 80$m. So $A_{trapezoid}=\frac{(100 + 200)\times80}{2}=\frac{300\times80}{2}=12000$ $m^{2}$.

Step4: Calculate total area

The total area of the field $A = A_{rectangle}+A_{trapezoid}=40000 + 12000=52000$ $m^{2}$.

Step5: Calculate number of sheep

The number of sheep $n=\frac{A}{2000}$, where $A = 52000$ $m^{2}$. So $n=\frac{52000}{2000}=26$.

Answer:

26