Answer:
42 square miles
Step-by-step explanation:
The area of a composite shape can be found by decomposing it into shapes whose area formulas you know. Here, the shape can be decomposed into a triangle and two rectangles. The two rectangles can be formed several ways.
Triangle
The area of the triangle at the top of the figure is ...
A = 1/2bh
A = 1/2(6 mi)(3 mi) = 9 mi²
Overall rectangle
The area of the overall rectangle (including the space at lower right) is ...
A = LW
A = (9 mi)(5 mi) = 45 mi²
Deleted space
The area of the rectangle at lower right that is not included in the shaded area is ...
A = LW
A = (4 mi)(3 mi) = 12 mi²
Total area
The total area of the figure is the sum of the triangle and overall rectangle, less the excluded area at lower right.
total area = 9 mi² +45 mi² -12 mi² = 42 mi²
The area of the figure is 42 square miles.
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Additional comment
Other ways to divide the figure into two rectangles are ...
- extend the vertical line to make a 9×2 and a 3×5 rectangle
- extend the horizontal line to make a 4×2 and a 5×5 rectangle
