what is the area of this figure? write your answer using decimals. use 3.14 for π. square kilometers

Explanation:

Step1: Divide the figure into rectangles and a quarter - circle

We can divide the figure into 3 rectangles and a quarter - circle.

Step2: Calculate the area of the first rectangle

The first rectangle has length $l_1 = 3$ km and width $w_1=2$ km. Area $A_1=l_1\times w_1=3\times2 = 6$ km².

Step3: Calculate the area of the second rectangle

The second rectangle has length $l_2=(3 + 5)$ km and width $w_2 = 8$ km. Area $A_2=l_2\times w_2=(3 + 5)\times8=64$ km².

Step4: Calculate the area of the third rectangle

The third rectangle has length $l_3 = 4$ km and width $w_3=7$ km. Area $A_3=l_3\times w_3=4\times7 = 28$ km².

Step5: Calculate the area of the quarter - circle

The radius of the quarter - circle $r = 3$ km. The area of a full - circle is $A_{circle}=\pi r^{2}$, so the area of a quarter - circle $A_4=\frac{1}{4}\pi r^{2}=\frac{1}{4}\times3.14\times3^{2}=\frac{1}{4}\times3.14\times9 = 7.065$ km².

Step6: Calculate the total area of the figure

$A = A_1+A_2+A_3+A_4=6 + 64+28+7.065=105.065$ km².

Answer:

$105.065$