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 first rectangle

The first rectangle has length \(8\) km and width \(6\) km.
The area of a rectangle is \(A = l\times w\), so \(A_1=8\times6 = 48\) square kilometers.

Step2: Calculate the area of the second rectangle

The second rectangle has length \(5\) km and width \(4\) km.
Using the formula \(A = l\times w\), \(A_2 = 5\times4=20\) square kilometers.

Step3: Calculate the area of the quarter - circle

The radius of the quarter - circle \(r = 9\) km.
The area of a full - circle is \(A=\pi r^{2}\), so the area of a quarter - circle is \(A_3=\frac{1}{4}\pi r^{2}\).
Substitute \(r = 9\) into the formula: \(A_3=\frac{1}{4}\times\pi\times9^{2}=\frac{81\pi}{4}\approx\frac{81\times3.14}{4}=63.585\) square kilometers.

Step4: Sum up the areas

The total area \(A=A_1 + A_2+A_3\).
\(A=48 + 20+63.585=131.585\approx131.59\) square kilometers.

Answer:

\(131.59\)