Question

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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Answer 1

To find the area of the composite figure, we need to break it down into its constituent rectangles and calculate their areas individually.

1. Bottom Rectangle:

   • Width = 7 miles
   • Height = 3 miles (since the left side extends upward)
   • Area = Width × Height = 7 miles × 3 miles = 21 square miles.

2. Left Rectangular Extension:

   • Width = 6 miles (left side vertical height)
   • Height = 3 miles (the height of this part)
   • Area = Width × Height = 6 miles × 3 miles = 18 square miles.

3. Right Rectangular Extension:

   • Width = 1 mile
   • Height = 1 mile (the vertical and horizontal lengths of this part)
   • Area = Width × Height = 1 mile × 1 mile = 1 square mile.

Now, we add the areas of all these rectangles together:

• Area of Bottom Rectangle = 21 square miles
• Area of Left Rectangular Extension = 18 square miles
• Area of Right Rectangular Extension = 1 square mile

Total Area = 21 + 6 + 1 = 28 square miles.

Therefore, the area of the composite figure is 28 square miles.