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 large rectangle with length \(6\) km and width \(5\) km, \(A_1=5\times6 = 30\) square kilometers.
For the small rectangle with length \(3\) km and width \(2\) km, \(A_2 = 3\times2=6\) square kilometers. There are two such small rectangles, so \(A_{2 - total}=2\times6 = 12\) square kilometers.

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, the formula is \(A=\frac{1}{4}\pi r^{2}\), where \(r = 9\) km.
\(A_3=\frac{1}{4}\times\pi\times9^{2}=\frac{81\pi}{4}\approx\frac{81\times3.14}{4}=\frac{254.34}{4}=63.585\) square kilometers.

Step3: Sum up the areas

The total area \(A=A_1 + A_{2 - total}+A_3\).
\(A=30 + 12+63.585=105.585\approx105.59\) square kilometers.

Answer:

\(105.59\)