Triangle Shape and Area
In this lesson, students construct triangle shapes with a given base on the geoboard, and determine their areas (one small square on the geoboard represents one square unit of area) with the objective of generalizing the triangle area formula. Triangles are also classified according to their shape, and the attributes of various types of triangles are explored. Here are some examples of the triangles the students explore:
One of the discoveries students make is that all triangles with the same height have equal areas. Using some of the ideas from areas of more complex shapes a special relationship between the triangles and an enclosing rectangle evolves... can you see what that is?
By exploring triangles on a dot grid, students determine that the same relationship holds true even when the apex of the triangle is not directly above the base of the triangle.
Students explore the areas and attributes of the following types of triangles:
A solid understanding of triangle geometry is important for later work with constructions and euclidean geometry. The isoceles triangle, especially, forms the basis of some of the classic geometric compass-and-straight-edge constructions.