To find the area of the composite shape described in your question, we can break the shape down into rectangles.
Based on the description:
- The horizontal line at the top measures 4 miles.
- The vertical line on the left measures 2 miles.
- There’s another horizontal line to the right that also measures 2 miles.
- The vertical line dropping to the bottom right also measures 2 miles.
Let's summarize the structure as follows:
- The left rectangle is formed by the top width of 4 miles and the height of 2 miles.
- The vertical height down the left edge is 2 miles.
- The dimensions of the right side are also 2 miles in height and 2 miles in width horizontally going right.
To calculate the area of the entire shape:
-
Left rectangle: \[ \text{Area} = \text{width} \times \text{height} = 4 \text{ miles} \times 2 \text{ miles} = 8 \text{ square miles} \]
-
Right rectangle: Here, the width is 2 miles and height is also 2 miles: \[ \text{Area} = \text{width} \times \text{height} = 2 \text{ miles} \times 2 \text{ miles} = 4 \text{ square miles} \]
Now, add the areas of both rectangles together: \[ \text{Total Area} = \text{Area of left rectangle} + \text{Area of right rectangle} \] \[ \text{Total Area} = 8 \text{ square miles} + 4 \text{ square miles} = 12 \text{ square miles} \]
Therefore, the area of the city is 12 square miles.