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Region I and II are squares. If region I has an area of 16 and region II has an area of 64 , what is the area of region III? A. 16 B. 50 C. 80 D. 512

Region I and II are squares. If region I has an area of 1616 and region II has an area of 6464, what is the area of region III?\newlineA. 1616\newlineB. 5050\newlineC. 8080\newlineD. 512512

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Full solution

Q. Region I and II are squares. If region I has an area of 1616 and region II has an area of 6464, what is the area of region III?\newlineA. 1616\newlineB. 5050\newlineC. 8080\newlineD. 512512
  1. Calculate Side Length of Region I: Region I is a square with area 1616, so one side is 16=4\sqrt{16} = 4 units.
  2. Calculate Side Length of Region II: Region II is a square with area 6464, so one side is 64=8\sqrt{64} = 8 units.
  3. Calculate Area of Region III: Region III is the difference in area between Region II and Region I, so area of Region III == area of Region II −- area of Region I.
  4. Calculate Area of Region III: Region III is the difference in area between Region II and Region I, so area of Region III == area of Region II −- area of Region I.Calculate the area of Region III: 64−16=4864 - 16 = 48.

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