Option C: [tex]$148 \mathrm{in}^{2}$[/tex] is the area of the trapezoid.
Explanation:
The image of the trapezoid having these descriptions is attached below:
Now, we shall determine the area of the trapezoid using the formula,
[tex]$A=\frac{a+b}{2} h$[/tex] where a and b are the base of the trapezoid and h is the height of the trapezoid.
Thus, we shall find the value of a and b from the diagram given below.
[tex]a= AB=14in[/tex]
[tex]b=DC\\b=DF+FE+EC\\b=3+14+6\\b=23in[/tex]
It is given that the height of the trapezoid [tex]h=8in[/tex]
Thus, substituting the values of a,b and h in the formula [tex]$A=\frac{a+b}{2} h$[/tex], we get,
[tex]A=\frac{14+23}{2}(8)\\ A=\frac{37}{2} (8)\\A=148in^2[/tex]
Thus, the area of the trapezoid is [tex]$148 \mathrm{in}^{2}$[/tex]
Hence, Option C is the correct answer.
