what is the area of this figure? provide an answer accurate to the nearest tenth. use 3.14 or a calculator…

Explanation:

Step1: Divide the figure into shapes

Divide the figure into a rectangle, a trapezoid and a triangle.

Step2: Calculate the area of the rectangle

The rectangle has length $l = 18$ cm and width $w=8$ cm. The area formula for a rectangle is $A_{rect}=l\times w$. So $A_{rect}=18\times8 = 144$ $cm^{2}$.

Step3: Calculate the area of the trapezoid

The trapezoid has bases $b_1 = 8$ cm, $b_2=10$ cm and height $h = 14 - 2=12$ cm. The area formula for a trapezoid is $A_{trap}=\frac{(b_1 + b_2)h}{2}$. So $A_{trap}=\frac{(8 + 10)\times12}{2}=\frac{18\times12}{2}=108$ $cm^{2}$.

Step4: Calculate the area of the triangle

The triangle has base $b = 4$ cm and height $h = 6$ cm. The area formula for a triangle is $A_{tri}=\frac{1}{2}bh$. So $A_{tri}=\frac{1}{2}\times4\times6 = 12$ $cm^{2}$.

Step5: Calculate the total area

The total area $A$ of the figure is the sum of the areas of the rectangle, trapezoid and triangle. $A=A_{rect}+A_{trap}+A_{tri}=144 + 108+12=264$ $cm^{2}$.

Answer:

$264.0$ $cm^{2}$