The area of a circle is given by $A=\pi r^2$. Since the diameter is $12$, the radius is half of that, or $6$. Substituting gives $A=\pi (6{)}^2=36\pi$. So the equivalent expression is $36\pi$.

The horizontal side length is the difference in the $x$-coordinates: $8-2=6$. The vertical side length is the difference in the $y$-coordinates: $5-1=4$. The area of a rectangle is length times width, so the area is $6\cdot 4=24$. Therefore, the correct answer is $24$.

Let the width be $w$ inches, so the length is $w+3$. Since the perimeter is 26,

Simplify:

Then the length is $5+3=8$. The area is

square inches. So the correct answer is $40$.

The area of a rectangle is found by multiplying length by width. Compute each poster's area:
- Poster 1: $8\times 6=48$ square inches
- Poster 2: $10\times 5=50$ square inches
- Poster 3: $7\times 9=63$ square inches
- Poster 4: $12\times 4=48$ square inches

The greatest area is $63$ square inches, so Poster 3 is the correct answer.

The area of a circle is found with the formula $A=\pi r^2$. Since the radius is $4$, substitute $4$ for $r$: $A=\pi (4{)}^2=\pi (16)=16\pi$. Therefore, the statement that must be true is that the area is $16\pi$ square inches.