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

31 square miles
31 square miles

28 square miles
28 square miles

21 square miles
21 square miles

25 square miles
25 square miles
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1 answer

To calculate the area of the composite figure, we will break it down into simpler shapes and find their areas individually before summing them up.

Here’s the breakdown:

  1. Bottom rectangle:

    • Width = 7 miles
    • Height (this is the height of the main rectangle) = 6 miles
    • Area = width × height = 7 miles × 6 miles = 42 square miles.
  2. Left side rectangular extension:

    • Width (horizontal length) = 3 miles
    • Height (vertical length) = 6 miles (this is the height of the original rectangle)
    • Area = width × height = 3 miles × 3 miles = 9 square miles.
  3. Right side rectangular extension:

    • Width (horizontal length) = 1 mile
    • Height (vertical length) = 1 mile
    • Area = width × height = 1 mile × 1 mile = 1 square mile.

Now we add all these areas together:

  • Total Area = Area of bottom rectangle + Area of left extension + Area of right extension
  • Total Area = 42 square miles + 9 square miles + 1 square mile = 52 square miles.

However, in the context of your question and the available answer choices, I believe there might be an oversight in identifying the dimensions of the composite figure or possible overlaps. If the area of just the main base rectangle (42 square miles) is used with subtracting other areas (if any overlap appears in a more complex example), please clarify the specifics so I can assist accurately.

Given your response options are:

  • 31 square miles
  • 28 square miles
  • 21 square miles
  • 25 square miles

I would need to adjust or clarify the dimensions provided for accurate alignment, but overall combined without further modification remains at 52 square miles from breakdown shown unless overlaps or subtractions are requisite to the subsequent figures asked.

Please review to ensure accurate detail or check if other constraints are placed before proceeding with selected option voluntarily listed.