The area of a triangle is found with the formula $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height. Substituting the given values gives $A=\frac{1}{2}(12)(9)=6\cdot 9=54$. Therefore, the area of the banner is $54$ square inches.

The area of a circle is found with the formula $A=\pi r^2$. The diameter is 10 feet, so the radius is half of that: $r=5$. Then

So the correct answer is $25\pi$.

Use the area formula for a circle: $A=\pi r^2$. Since the area is $16\pi$, set $\pi r^2=16\pi$. Dividing both sides by $\pi$ gives $r^2=16$, so $r=4$. Then use the circumference formula, $C=2\pi r$. Substituting $r=4$ gives $C=2\pi (4)=8\pi$. Therefore, the correct answer is $8\pi$.

Because one side of the rectangle lies on the x-axis and one side lies on the y-axis, the rectangle’s vertices are $(0,0)$, $(6,0)$, $(0,4)$, and $(6,4)$. Its length is 6 units and its width is 4 units. The area of a rectangle is length times width, so the area is $(6)(4)$. Therefore, the equivalent expression is $(6)(4)$.

The area of the rectangle is $12\cdot 5=60$ square inches. Since the triangle has the same area, its area is also 60. Let the triangle's base be $5+x$ because it is $x$ inches longer than the rectangle's width. Using the triangle area formula,

Since $\frac{1}{2}\cdot 8=4$, this becomes

Divide by 4:

Subtract 5: