https://file.aiquickdraw.com/mathbot/file/1726685005624o3ht4m2i.jpg

Let's break down the problem based on the trapezoidal diagram provided and solve it step by step.

### Step 1: **Finding the Area of the Dry Land**

The shape of the dry land (the lighter trapezoid) is a **trapezoid**. The formula to find the area of a trapezoid is:

\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]

Where:
- \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides.
- \( h \) is the height of the trapezoid.

From the diagram:
- \( b_1 = 7 \) miles (bottom base)
- \( b_2 = 5 \) miles (top base)
- \( h = 10 \) miles (height)

Now, we can plug in the values:

\[
A = \frac{1}{2} \times (7 + 5) \times 10 = \frac{1}{2} \times 12 \times 10 = 60 \, \text{square miles}
\]

### Step 2: **Finding the Population Density**

The population living in the dry land is given as **79,626 people**. Population density \( D \) is calculated as:

\[
D = \frac{\text{Population}}{\text{Area of dry land}}
\]

Substituting the values we know:

\[
D = \frac{79,626}{60} \approx 1,327.1 \, \text{people per square mile}
\]

### Final Answers:
1. **The area of dry land** is 60 square miles.
2. **The equation to find population density** is \( D = \frac{79,626}{60} \).

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Let me know if you'd like more details or clarifications! Here are five related questions to expand on this:

1. How does changing the height of the trapezoid affect the area?
2. What would the area be if the top base was reduced to 3 miles?
3. How would the population density change if the area of the dry land was halved?
4. What is the difference in population density if the population increases by 10,000 people?
5. How does the population density compare between the dry land and a hypothetical area twice its size?

**Tip:** For trapezoidal shapes, always check the lengths of the parallel sides carefully, as they define the bases in the area formula!

In the rectangle below, each of the given measures represent miles. The lighter area represents dry land, and the darker area represents land covered by water. The population of people living in the dry land is 79,626 people. Complete the sentences: The area of dry land, in square miles, is ___ . The equation to find the population density D, of the dry land is ___ .

Learn how to calculate the area of a trapezoid and determine population density based on the population of 79,626 people. This geometry problem focuses on trapezoidal area calculation and population density formula, suitable for Grades 6-8.

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