9514 1404 393
Answer:
Step-by-step explanation:
The Pythagorean theorem (see Hint) tells you the length of the hypotenuse (c) is ...
c² = 1² + 1² = 2
c = √2 ≈ 1.4142136 . . . units
The estimated value of the length of the hypotenuse is 1.41 units.
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Of course the shaded square will have an area that is the square of that value:
area = s² ≈ 1.41² ≈ 1.99 . . . . . rounded to hundredths
The estimated area of the square is 1.99 square units.
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<em>Additional comment</em>
Of course, we don't have to estimate. We can use the exact value of the side length to determine the shaded square has an area of ...
area = s² = (√2)² = 2 . . . . exactly
We can also get there by recognizing that the lengths of 1 represent half the length of each of the diagonals of the square. That is, the square's diagonals are both of length 2. The area is half their product, so is (1/2)(2·2) = 2 square units.
