Question

what is the area?
write your answer as a fraction or as a whole or mixed number.
2 mi
5\frac{2}{3} mi
2 mi
square miles

Explanation:

Step1: Identify the shape and formula

The figure is a trapezoid. The formula for the area of a trapezoid is $A = \frac{(b_1 + b_2)}{2} \times h$, where $b_1$ and $b_2$ are the lengths of the two parallel sides (bases), and $h$ is the height (the perpendicular distance between the bases). Here, $b_1 = 2$ mi, $b_2 = 2$ mi, and $h = 5\frac{2}{3}$ mi. Wait, actually, looking at the diagram, maybe it's a rectangle? Wait, no, the two parallel sides (top and bottom) are both 2 mi, and the height is $5\frac{2}{3}$ mi. Wait, if both bases are equal, then it's a rectangle? Wait, no, a trapezoid with equal bases is a rectangle. Wait, maybe the diagram is a trapezoid with $b_1 = 2$, $b_2 = 2$, so average of bases is 2, times height. Wait, no, maybe I misread. Wait, the top base is 2 mi, bottom base is 2 mi, and the height is $5\frac{2}{3}$ mi. So actually, it's a rectangle? Wait, no, a rectangle has four right angles, and if the two parallel sides are equal, then it's a rectangle. Wait, but the formula for the area of a trapezoid when $b_1 = b_2$ is the same as a rectangle: $A = b \times h$, since $\frac{(b + b)}{2} = b$. So let's confirm: the two parallel sides (bases) are both 2 mi, and the height (distance between them) is $5\frac{2}{3}$ mi. So area is base times height? Wait, no, in a trapezoid, the area is average of the two bases times height. If both bases are 2, then average is 2, so $A = 2 \times 5\frac{2}{3}$. Wait, but maybe the diagram is a trapezoid with $b_1 = 2$, $b_2 = 2$, so it's a rectangle. So let's proceed.

Step2: Convert the mixed number to an improper fraction

The height $h = 5\frac{2}{3}$ mi. To convert to an improper fraction: $5\frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{17}{3}$ mi.

Step3: Calculate the area

Using the formula for the area of a trapezoid (or rectangle, since bases are equal): $A = \frac{(b_1 + b_2)}{2} \times h$. Here, $b_1 = 2$, $b_2 = 2$, so $\frac{(2 + 2)}{2} = 2$. Then $A = 2 \times \frac{17}{3} = \frac{34}{3}$. Convert back to a mixed number: $\frac{34}{3} = 11\frac{1}{3}$. Wait, wait, no: $2 \times 5\frac{2}{3} = 2 \times \frac{17}{3} = \frac{34}{3} = 11\frac{1}{3}$. Wait, but let's check again. Wait, maybe the two bases are not both 2. Wait, maybe the top base is 2, bottom base is 2, and the height is $5\frac{2}{3}$. Wait, but if it's a trapezoid with both bases 2, then it's a rectangle, so area is length times width. Wait, maybe the diagram is a trapezoid with $b_1 = 2$, $b_2 = 2$, so area is $\frac{(2 + 2)}{2} \times 5\frac{2}{3} = 2 \times 5\frac{2}{3} = 10 + \frac{4}{3} = 11\frac{1}{3}$. Wait, that makes sense.

Wait, let's do the calculation again. $5\frac{2}{3}$ is equal to $\frac{17}{3}$. Multiply by 2: $2 \times \frac{17}{3} = \frac{34}{3}$. Convert $\frac{34}{3}$ to a mixed number: 34 divided by 3 is 11 with a remainder of 1, so $11\frac{1}{3}$.

Answer:

$11\frac{1}{3}$