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

Explanation:

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

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

Step2: Calculate the area of the first rectangle

The first rectangle has length $l_1 = 15$ mm and width $w_1=8$ mm. Its area $A_1=l_1\times w_1=15\times8 = 120$ $mm^2$.

Step3: Calculate the area of the second rectangle

The second rectangle has length $l_2 = 7$ mm and width $w_2 = 6$ mm. Its area $A_2=l_2\times w_2=7\times6=42$ $mm^2$.

Step4: Calculate the area of the third rectangle

The third rectangle has length $l_3 = 4$ mm and width $w_3 = 16$ mm. Its area $A_3=l_3\times w_3=4\times16 = 64$ $mm^2$.

Step5: Calculate the area of the quarter - circle

The radius of the quarter - circle $r = 4$ mm. The area of a full - circle is $A_{circle}=\pi r^{2}$, so the area of the quarter - circle $A_4=\frac{1}{4}\pi r^{2}=\frac{1}{4}\times3.14\times4^{2}=\frac{1}{4}\times3.14\times16 = 12.56$ $mm^2$.

Step6: Calculate the total area of the figure

The total area $A = A_1+A_2+A_3+A_4=120 + 42+64+12.56=238.56$ $mm^2$.

Answer:

$238.56$