Answer :
Let's begin by identifying key information given to us:
The figure is a trapezoid
base (1) = 70 1/2 in = 70.5 in
base (2) = 65 1/2 in = 65.5 in
area = 1224 in sq
To solve for the height, we will follow these steps:
[tex]\begin{gathered} A=(\frac{a+b}{2})h \\ A=1224in^2,a=70\frac{1}{2}in\text{ or 70.5 in},b=65\frac{1}{2}in\text{ or 65.5 in},h=\text{?} \\ 1224=\frac{\mleft(70.5+65.5\mright)}{2}_{}h\Rightarrow1224=\frac{136}{2}h \\ 1224\cdot2=136h\Rightarrow136h=2448 \\ \Rightarrow h=\frac{2448}{136}=18 \\ h=18in \\ \\ \therefore The\text{ height of the countertop is }18in \end{gathered}[/tex]Therefore, the height of the countertop is 18 inches