Grade 9s looked at rectangles with a perimeter of 24 today. We learned that there are many ways to make a rectangle with perimeter 24, and that they don’t all have the same area.

Important to note: a rectangle has 4 right angles, by definition, so a square is a kind of rectangle.

We arranged the rectangles on a graph. Horizontal dimension was the independent variable, and Area was the dependent variable. We used the rectangles as the dots.

We noticed that in all of the diagrams, the rectangle with the biggest area was the square. We noticed that it’s a non-linear graph, and it’s positive for a while, and then it becomes negative. The graph is also direct, since a rectangle with a horizontal dimension of 0 would have an area of 0 also.

We answered some questions about maximum area, or minimum perimeter for quadrilaterals.

We need to have a good understanding of perimeter, area, and how making a quadrilateral more square, or more snake-like will affect the area/perimeter.

We learned that sometimes we will need to use the square root to find the square’s dimensions, if given the area.