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Sagot :

Answer:

18 mi^2

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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
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