c Divide the number of goats by the number of square meters.
A
a About 74.24 m^2
B
b About 36.2 m
C
c About 0.08 goats per square meter
Practice makes perfect
a Given what we see in the diagram, we can add some additional information.
The area of the petting zoo is the area of the sector in the upper left corner subtracted from the area of the trapezoid that can be identified in the diagram. To find the area of the trapezoid, we have to find the full length of the second horizontal side. Let's add some additional information to the diagram.
Now we can find the length of the shorter leg by using the tangent ratio.
The short leg of the right triangle is 1.7 meters. This means the full length of the trapezoid's second parallel side is 10+1.7=11.7 meters. With this information we can calculate the area of the trapezoid.
Finally, we will subtract the area of the sector from the area of the trapezoid to find the area of the zoo pen.
86.8-12.57 =74.23m^2
b To determine how many meters of fence is needed to enclose the zoo, we have to find the length of the remaining side and the curved part of the sector.
Examining the diagram, we see that the remaining side of the trapezoid is also the hypotenuse of a right triangle. Using the sine ratio we can find the length of this distance, which we have labeled y.
Next we will find the perimeter of the sector by calculating the circumference of a circle with a diameter of 8 meters and multiplying this by its central angle divided by 360^(∘).
P= 8π(90^(∘)/360^(∘)) ≈ 6.28 m
When we have all of the sides, we can find the perimeter.
6.28+ 6+8.18+11.7+4≈ 36.2 m
c The density of goats in the pen is the number of goats per square meter — we have to divide the number of goats by the number of square meters.
6/74.24≈ 0.08
The density is 0.08 goats per square meter.
