Use the image to answer the question.

A composite shape is drawn. The vertical width on the left side from top to bottom shows no measurement. The shape is drawn with straight lines and right angles. A horizontal line marked 4 miles is drawn from the upper left corner. A vertical line marked 2 miles drops down from the the top horizontal line. A horizontal line marked 2 miles continues to the right. A vertical line marked 2 miles drops down to become the right edge of the shape. A horizontal line of unknown length is drawn leftward. A vertical line marked 2 miles drops down to the base. A baseline marked 2 miles meets the width side to form the lower left corner.

A city map is shown. What is the area of the city in square miles?

1 answer

To find the area of the composite shape described in your question, we can break the shape down into rectangles.

Based on the description:

  1. The horizontal line at the top measures 4 miles.
  2. The vertical line on the left measures 2 miles.
  3. There’s another horizontal line to the right that also measures 2 miles.
  4. 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:

  1. Left rectangle: \[ \text{Area} = \text{width} \times \text{height} = 4 \text{ miles} \times 2 \text{ miles} = 8 \text{ square miles} \]

  2. 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.