On a sectional chart, used for aviation navigation, a military operating zone has the shape of a trapezoid. One base is 20 mi in length; the other base is 18 mi. The lengths of the other two sides are 12.24 mi and 13.1 mi. The distance between the parallel sides is 11.4 mi. What is the perimeter and the area of the military operating zone?
A) $P = 63.3 \mathrm { mi }$
B) $P = 59.3 \mathrm { mi }$
C) $P = 74.7 \mathrm { mi }$
D) $A = 217 \mathrm { mi } ^ { 2 }$
E) $A = 370 \mathrm { mi } ^ { 2 }$
F) $A = 350 \mathrm { mi } ^ { 2 }$

Question

Quizplus · Accepted Answer

The perimeter $P$ is the sum of all sides: $20 + 18 + 12.24 + 13.1 = 63.34 \mathrm { mi }$, which rounds to $63.3 \mathrm { mi }$. The area $A$ of a trapezoid is given by $\frac{1}{2}(b_1 + b_2)h$, where $b_1$ and $b_2$ are the lengths of the bases, and $h$ is the height. Substituting the given values, $A = \frac{1}{2}(20 + 18) \times 11.4 = 19 \times 11.4 = 216.6 \mathrm { mi }^2$, which rounds to $217 \mathrm { mi }^2$.

On a Sectional Chart, Used for Aviation Navigation, a Military P=63.3miP = 63.3 \mathrm { mi }P=63.3mi

On a Sectional Chart, Used for Aviation Navigation, a Military $P = 63.3 \mathrm { mi }$