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

Explanation:

Step1: Divide the figure into shapes

Divide the figure into a rectangle, a smaller rectangle and a quarter - circle.

Step2: Calculate the area of the first rectangle

The first rectangle has length $l_1 = 7$ ft and width $w_1=3$ ft. The area formula for a rectangle is $A = lw$. So $A_1=7\times3 = 21$ square - feet.

Step3: Calculate the area of the second rectangle

The second rectangle has length $l_2=(5 + 2)$ ft and width $w_2 = 6$ ft. So $A_2=(5 + 2)\times6=42$ square - feet.

Step4: Calculate the area of the quarter - circle

The radius of the quarter - circle $r = 8$ ft. The area formula for a full - circle is $A=\pi r^{2}$, and for a quarter - circle $A_3=\frac{1}{4}\pi r^{2}$. Substituting $r = 8$ ft and $\pi=3.14$, we get $A_3=\frac{1}{4}\times3.14\times8^{2}=\frac{1}{4}\times3.14\times64 = 50.24$ square - feet.

Step5: Calculate the total area

The total area $A = A_1+A_2+A_3$. So $A=21 + 42+50.24=113.24$ square - feet.

Answer:

$113.24$