Area of a Triangle: Hands-on Math

We did a simple hands-on activity to prove the area of any triangle is 1/2 the area of a rectangle.

This activity came from the Murderous Maths book Savage Shapes. (Great series, bad title.) In the UK math is maths. This British series discusses pre-algebra level math concepts in story format. The books feel more like comic books than text books. They are quirky and entertaining, yet educational. I highly recommend you check them out.

To begin this activity sketch three parallel lines. Then measure four draw marks the same distance on the center line to serve as the base for the shapes. Perhaps 1.5 inches. Next draw two perpendiculars extending from the first base to create a rectangle. Connect the base lines for the second base to a point in the center of the base above the line (and below the line) to create two isosceles triangles. The third base should be connected to a point above one endpoint to create a right triangle. The final base should be connected to a point outside the base to create an obtuse triangle.

Cut out the shapes. 2 rectangles, 6 triangles. (Only 1 rectangle is needed)

Place each pair of triangles on top of the rectangle to fully cover the area. This shows that the area of one triangle is equal to the area of 1/2 of the rectangle.

Note: It will be necessary to cut some of the triangles in order for them to fit onto the rectangle.