Answer
a) $18\text{ ft}^2$
b) $6\text{ ft}; 3\text{ ft}$
Work Step by Step
$a) $
Let the area of one rectangular mat be $x$. Then the area of square will be $\dfrac{x}{2}$.
Total area of four rectangular mat and one square is $81$:
$$x+x+x+x+\frac x2=81$$
$$4x+\frac{x}{2}=81$$
$$2\left(4x+\frac{x}{2}\right)=2(81)$$
$$8x+x=162$$
$$9x=162$$
$$x=162:9=18$$
Area of one rectangular mat is $18~\text{ft}^2$.
$b)$
Let the length be $8$ and width be $4$. Check the product:
$$8\times 4=32$$
It is not $18$.
Now check $6$ and $3$:
$$6\times 3=18$$
So, $6$ and $3$ are dimensions of rectangle in feet.
