By Page Bird

A Triangle in a Rectangle

A triangle has two shared vertices and one shared side with a rectangle. The third vertex is anywhere on the side opposite of the shared side.


How does the area of the triangle compare with the area of the rectangle? Why do you think this relationship holds?


This relationship always holds because the base and the height of the triangle stay the same regardless of where the third vertex lies on the rectangle.

So at all times the base of the given triangle is the same and the height of the triangle is also the same. The triangle will always have a 1-to-2 ratio with the rectangle.

Click here to see a GSP sketch.

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