what is the area of this figure?\nif necessary, round your answer to the nearest hundredth.\nsquare 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)