Question

what is the area of this figure?
if necessary, round your answer to the nearest hundredth.
square kilometers

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\).
For the vertical rectangle: length \(l=(3 + 3+3)=9\) km, width \(w = 3\) km. Area \(A_1=9\times3 = 27\) \(km^{2}\).
For the horizontal rectangle (excluding the overlapping part with the vertical rectangle): length \(l = 5\) km, width \(w=3\) km. Area \(A_2 = 5\times3=15\) \(km^{2}\).

Step2: Calculate the area of the quarter - circle

The formula for the area of a circle is \(A=\pi r^{2}\). For a quarter - circle, \(A=\frac{1}{4}\pi r^{2}\), where \(r = 10\) km.
\(A_3=\frac{1}{4}\times\pi\times10^{2}=\frac{1}{4}\times3.14\times100 = 78.5\) \(km^{2}\)

Step3: Calculate the total area

The total area \(A=A_1 + A_2+A_3\)
\(A=27+15 + 78.5\)
\(A=120.5\) \(km^{2}\)

Answer:

\(120.5\)