SAT Question 8c1aa743: Area and Volume answer and explanation with Desmos solution

Choice D is correct. The area of a rectangle is given by $bh$, where $b$ is the length of the base of the rectangle and $h$ is its height. Let $x$ represent the length, in units, of the base of rectangle $\text{ABCD}$, and let $y$ represent its height, in units. Substituting $x$ for $b$ and $y$ for $h$ in the formula $bh$ yields $xy$. Therefore, the area, in square units, of $\text{ABCD}$ can be represented by the expression $xy$. It's given that the length of each side of $\text{EFGH}$ is $6$ times the length of the corresponding side of $\text{ABCD}$. Therefore, the length, in units, of the base of $\text{EFGH}$ can be represented by the expression $6x$, and its height, in units, can be represented by the expression $6y$. Substituting $6x$ for $b$ and $6y$ for $h$ in the formula $bh$ yields $\left(6x\right)\left(6y\right)$, which is equivalent to $36xy$. Therefore, the area, in square units, of $\text{EFGH}$ can be represented by the expression $36xy$. It's given that the area of $\text{ABCD}$ is $54$ square units. Since $xy$ represents the area, in square units, of $\text{ABCD}$, substituting $54$ for $xy$ in the expression $36xy$ yields $36\left(54\right)$, or $1,944$. Therefore, the area, in square units, of $\text{EFGH}$ is $1,944$.