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The area of the rectangle is the length of the perpendicular sides (ie the sides which meet at right angles) multiplied together.

This could be solved by using Pythagoras to find the lengths of the two sides between the given points, but a quick inspection shows that the rectangle is aligned orthogonally (ie parallel to the x- and y-axes) and so only the difference between the corresponding x- and y- coordinates need be calculated before multiplying together.

  • The side between (1, 9) and (6, 9) has a length of (6 - 1) = 5 units
  • The side between (6, 4) and (6, 9) has a length of (9 - 4) = 5 units
→ area of the rectangle = 5 units × 5 units = 25 square units.

Note: as the perpendicular sides are equal, all four sides are equal in length and this is the special rectangle which is called a square.

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7y ago
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7y ago

The given coordinates are not those of a rectangle but a square, whose area is 25.

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Q: What is the area of a rectangle with three of its vertices at 1 9 and 6 4 and 6 9?
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