Paper tearing activity: Students
will create a rectangle of their choice. After discussing the area of a
rectangle, students will tear their rectangle in half, This will be done
by tearing along a diagonal of the rectangle. Students will notice that
the area of each triangle is the same, thus discovering a formula for the
area of a triangle.
Pick's Formula: Area of a triangle equals the number of points which lies on the border plus the number of points which lie within the border minus 1 (this is when the triangle is placed on a grid like a geoboard).
Solve for the area of the following polygons:
For each of the following triangles, Use Pick's Formula for finding its area.
10.
11.
12.
Find some other method used to find the area of a triangle, besides a=1/2(base)(height) or Pick's Formula. Below are some possibilities:
Heron's Formula
Area of Circumscribed rectangle
Use of Vectors
CHALLENGE #2:
Develop on your own, a new method for finding the area of a triangle.
Write a short essay on how the area of a triangle and a rectangle relate.