Triangle Area

About the activity

Manipulate the vertices to make a triangle of any desired shape. See that whatever shape is chosen, by appropriately subdividing the resulting triangle, the shaded smaller triangles can be dragged to fill exactly half the area of the surrounding rectangle. (Take careful note of the piece shaded black when the midpoint of the longest side is outside the rectangle.)

The side lengths and angle sizes can be displayed as well, allowing validation of the formulas for the area: A= ½bh, A = ½ab sin C and Heron's formula.

Related...

Exploring triangle area

Manipulate the triangle by dragging the vertices.

Hit the Subdivide button to divide the triangle into smaller pieces.

Explore the relationship between the triangle and rectangle areas by dragging and rotating the coloured pieces to fit exactly onto the rectangle.

Use the Angles and Lengths buttons to hide or show the angle sizes and side lengths respectively.

Select the Vertex transformation button to move triangle vertices (this is the default), or one of the other transformation buttons to manipulate the triangle without changing the angles.