Triangles Inside a Rectangle

Examine the area and perimeter of a triangle compared to a rectangle.

Rationalize this!: Find the a right triangle with rational side lengths, and a hypotenuse numerically equal to the area of the triangle.

Equal Areas: Determine why a certain rectangle has the same area as a triangle.

Optimal Triangles: Determine the largest area of a triangle given a restricted perimeter.

All Swimmed Out: Determine the shortest path in a noncollinear route using triangles.

The Third Side: What are the possible perimeters that a given triangle can have?

Casting Shadows: Use a man’s shadow to determine his distance from a tree.

Bouncing Barney: Follow Barney’s walking pattern to determine how many times he will reach a wall before returning to his starting point.

Transforming Triangle: What is the perimeter of a rectangle formed from an equilateral triangle?

Triangle in a Quadrilateral: Given the ratio of a quadrilateral’s length to width, find the ratio of the area of a special shaded region to the area of the quadrilateral.

What is this point?: Determine the properties associated with a special point inside a triangle.

Submit your idea for an investigation to InterMath.

Triangles in a Trapezoid

Determine the relationship between the areas of triangles formed by the diagonals of a trapezoid.


Make a triangle from a quadrilateral without changing the area.

Biggie Size It (Triangle)

Explore changes in the perimeter and area of a triangle when you increase its size.

Squaring with Squares

Draw area connections to the Pythagorean Theorem.

Capture the Flag

Locate the best starting position in a game of capture the flag.

Find the Hidden Treasure

Determine a shortcut to find a treasure inside of a triangle.