Points $A(2,1)$ and $B(8,1)$ have the same $y$-coordinate, so $\overline{AB}$ is a horizontal base. Its length is $8-2=6$. The height is the vertical distance from point $C(5,7)$ to the line $y=1$, which is $7-1=6$. Using the triangle area formula,

So the correct answer is $18$.

The volume of a cylinder is given by $V=\pi r^{2}h$. Since each jar's volume includes the same factor $\pi$, compare $r^{2}h$ for each jar.

For jar P: $3^2(10)=9\cdot 10=90$

For jar Q: $4^2(6)=16\cdot 6=96$

For jar R: $5^2(5)=25\cdot 5=125$

For jar S: $6^2(4)=36\cdot 4=144$

Because $144$ is the greatest value, jar S has the greatest volume. Therefore, the correct answer is D.

The volume of a cylinder is given by $V=\pi r^{2}h$. For the first cylinder, the volume is $V_1=\pi r^{2}h$. For the second cylinder, the radius is $2r$ and the height is $\frac{h}{2}$, so its volume is

Since $V_1=\pi r^{2}h$, it follows that $V_2=2V_1$. Therefore, the second cylinder has twice the volume of the first cylinder.

Find the area of the rectangle and the area of the semicircle, then add them. The rectangle has area $18\times 10=180$ square meters. The semicircle has diameter 10, so its radius is $5$. The area of the full circle would be $\pi r^2=\pi (5^2)=25\pi$, so the area of the semicircle is $\frac{25\pi }{2}\approx 39.27$. Adding gives $180+39.27\approx 219.27$, which rounds to $219$ square meters.

First find the area of the entire rectangular flower bed: $18\times 10=180$ square feet. Then find the area of the circular fountain: $\pi r^2=3.14(3^2)=3.14(9)=28.26$ square feet. The area left for planting is the rectangle's area minus the fountain's area: $180-28.26=151.74$. So the correct answer is $151.74$.