Shapes on the Grid: Princess Ruby's Rainbow Castle

Princess Ruby is planning new flower beds for her Rainbow Castle on a grid. She marks the corners of each bed as points, then joins them with straight lines to make squares and rectangles.

Remember: Each jump of 1 on a grid is 1 unit long. The side from (1, 2) to (5, 2) is 5 − 1 = 4 units long. A rectangle’s corners come in pairs: two corners share the same first number and two share the same second number. Its perimeter is all 4 sides added up, and its area is the grid squares inside.

Magic trick: For a rectangle’s missing corner, look at the other three: it takes the across number that shows up only once and the up number that shows up only once.