Area of triangles 2

The topic  is a topic under the 6th Grade Math Mission. This exercise practices finding the area of triangles that are not set up in a standard position.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the area of the triangle on the grid: This problem provides a triangle placed on a rectangular grid with all vertices sitting at lattice points. Most of the time, however, none of the sides are parallel to the directions of the grid. The student is asked to find the area of the triangle and write the answer in the space provided.Aot2-1.png

Strategies
Knowledge of the area of a triangle formula and an ability to complete a triangle into a rectangle are needed on this problem. It is also possible to do this problem using distance formula plus Heron's formula, but why?
 * 1) The formula for the area of a triangle is base times height divided by two, or one half of base times height.
 * 2) The triangle can be "completed" into a rectangle by inserting several right triangles in the corners. Then the area of the triangle itself can be found by subtracting the area of the right triangles from the overall rectangle.
 * 3) A calculator can be used to write a program to do this problem. Try to read the following code and understand how it finds the area:


 * Prompt, A,B,C,D,E,G
 * (A+B)->X
 * (C+D)->Y
 * (X-E)->F
 * (Y-G)->H
 * Disp XY-.5(AH+BC+DE+FG)