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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

21 square miles
21 square miles

31 square miles
31 square miles

25 square miles
25 square miles

Answer 1

To find the area of the composite figure, let's break it down based on the provided dimensions:

1. Main Rectangle:

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

2. Left Extension (Rectangle):

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

3. Right Extension (Rectangle):

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

Now we can combine the areas of all the rectangles:

Total Area = Area of Main Rectangle + Area of Left Extension + Area of Right Extension
Total Area = 42 + 18 + 1 = 61 square miles

It seems none of the provided choices are correct as the total computed area here is 61 square miles. If 61 square miles wasn't among the options you provided, please double-check the description or the options.