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On the following composite figure, all angles are right angles. All short edges of the figure have a measure of 1.5 centimeters. All long edges have a measure of 3 centimeters. Find the area of the figure. Explain or show how you got your answer.

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On The Following Composite Figure All Angles Are Right Angles All Short Edges Of The Figure Have A Measure Of 15 Centimeters All Long Edges Have A Measure Of 3 class=

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Answer:

  27 cm²

Step-by-step explanation:

There are many ways the figure can be decomposed into parts for which you know the area formula. The total area is the sum of the parts.

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decomposition

We recognize that each of the tabs is twice as long as wide, so is half a square. The 4 tabs together make 2 squares that are 3×3 cm. Of course, what remains after removing the tabs is a 3×3 cm square in the middle of the figure.

sum of parts

Then the total area is that of 3 squares measuring 3 cm × 3 cm:

  A = s² = (3 cm)² = 9 cm² . . . . . area of one square

  total area = 3A = 3(9 cm²) = 27 cm²

The area of the figure is 27 cm².

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Alternate solution

The figure can also be considered to be a 6 cm × 6 cm square with four 1.5 cm × 1.5 cm squares removed from its corners. Then the area is ...

  (6 cm)² -4(1.5 cm)² = (36 -4(2.25)) cm² = 27 cm²

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