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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

31 square miles
31 square miles

21 square miles
21 square miles

25 square miles

Answer 1

To find the area of the composite figure, we will calculate the area of each part and then sum them up.

1. Main rectangle:

   • Width: 7 miles
   • Height: 6 miles
   • Area = Width × Height = 7 miles × 6 miles = 42 square miles

2. Left rectangular extension:

   • Width: 3 miles
   • Height: 1 mile (the vertical height of the rectangle is 1 mile)
   • Area = Width × Height = 3 miles × 1 mile = 3 square miles

3. Right rectangular extension:

   • Width: 1 mile
   • Height: 1 mile
   • Area = Width × Height = 1 mile × 1 mile = 1 square mile

Now, to find the total area of the composite figure, we will sum the areas:

Total Area = Area of Main Rectangle + Area of Left Extension + Area of Right Extension = 42 square miles + 3 square miles + 1 square mile = 46 square miles

It seems that none of the options provided (28, 31, 21, 25 square miles) match this conclusion based on the dimensions you provided. Please double-check the dimensions or the calculations associated with the rectangles and extensions. If the dimensions or areas are incorrect, please let me know.