Lesson idea : The software provides an alternative way to find the area of a triangle.
Through exploration, students are expected to relate the area of a triangle to that of a bounding rectangle. The method described here is a novel one. It uses properties of midpoint of the slant sides of the triangle. Students are expected to verbalise their thought during the course of the exploration, to explain the method and to reach the formula for the area of a triangle.
Title Area of triangle
Topic Measurement
Teaching approach Inductive, Visualisation
Learning objectives Determine the formula for the area of a triangle
Explain the method used
Subject Mathematics
Age of students 8-9 years
Teacher note:
Rationale
(Read along with the geogebra file)
A triangle can be bounded within a rectangle. One of the sides of the rectangle being the base of the triangle and its side opposite to that base containing the apex of the triangle.
When the rectangle is divided horizontally into two equal parts, the dividing line cuts the slant sides of the triangles into two equal parts (i.e., at their midpoint). The triangle is split into a trapezium and a smaller upper triangle (see Geogebra activity). The upper triangle can now be split into two smaller triangles.
These, when rotated through 180 degrees about the midpoints obtained above, rearrange the area of the initial triangle into that of half the bounding rectangle.
Strategy
Students can be paired up. They can discuss the findings of their explorations. It is expected they undertake a number of trials by varying the dimensions of the triangle.
