Find the area of the shaded region between triangle ABC and triangle GHI, if the corresponding sides of the three triangles are paralle and 1 unit apart. Triangle DEF less midway between the other two triangles. The lengths of the sides of triangle DEF are 5,6 and 7 units. (See figure 1)
Student will initially try to find the area of triangles ABC and GHI and then taje the difference. Rather than pursue this method, lets look at the problem from another point of view. Consider the figure as cut into three trapezoids (AGIC, AGHB, and BCIH) as show in figure 2.
In each case, the altitude of the trapezoid is 2. The medians are 5,6 and 7, respectively. Thus, we apply the formula for the area of a trapezoid, A = median x height:
Trapezoid AGIC = 5 . 2 = 10
Trapezoid AGHB = 7 . 2 = 14
Trapezoid BCIH = 6 . 2 = 12
The total of the shaded region 10 +14 +12 = 36 squere units.