Question

Use the image to answer the question.

An illustration shows a rectangle extending upward on the top left and top right sides forming two more rectangles of varying width and length. The dimensions are as follows: The bottom of the rectangle is 7 miles. The extended left side is 6 miles. The vertical height of the left side rectangular extension is 3 miles. The vertical and horizontal lengths of the right side rectangular extension is 1 mile each. There are six right angle symbols at the vertices of the polygon.

What is the area of the composite figure?

(1 point)
Responses

28 square miles
28 square miles

25 square miles
25 square miles

31 square miles
31 square miles

21 square miles

Answer 1

To find the area of the composite figure, we can break it down into two parts: the main rectangle and the two rectangular extensions.

1. **Main Rectangle**:
- Width = 7 miles
- Height = 6 miles
- Area of the main rectangle = Width × Height = 7 miles × 6 miles = 42 square miles.

2. **Left Extension**:
- Width = 6 miles
- Height = 3 miles
- Area of the left extension = Width × Height = 6 miles × 3 miles = 18 square miles.

3. **Right Extension**:
- Width = 1 mile
- Height = 1 mile
- Area of the right extension = Width × Height = 1 mile × 1 mile = 1 square mile.

Now, we add the areas of the main rectangle and both extensions:

Total Area = Area of main rectangle + Area of left extension + Area of right extension
Total Area = 42 square miles + 18 square miles + 1 square mile = 61 square miles.

However, it seems there may have been a misunderstanding in the descriptions of the dimensions, as the provided responses suggest significantly smaller areas.

Please check again if we need to subtract or if there are specific shapes that were not considered in their entirety. The dimensions provided yield an area of 61 square miles based on the calculation presented.

Given the provided answer choices (28, 25, 31, 21 square miles), it seems the total area calculated from the detailed description exceeds the provided options. Reassessing the descriptions may be necessary for correctness in determining the area for typical answer responses.