Fdambro294 wrote:
Amazing question......relies on 2 rules and understanding the figure.
Rule 1: there exists only one value for the perpendicular height between 2 parallel lines
Rule 2: given that 2 triangles have the same base, the ratio of the areas of those triangles will depend on the ratio of the respective Heights drawn to the common Base
S1 and s2 don’t give you enough information to solve the question.
However, after filling in the points for A , B, C, and D
You will see that Point E must lie on the vertical line that passes through X = 6 right through Point B (6 , 0)
Placing E on the line X = 6 at a point in between (6 , 20) and (6 , -12) you can see from the figure that both quadrilateral ABCD and AECD will have as common the triangular area given by Points A, D and C along with the Y Axis.
The rest of the area of the quadrilateral ABCD will be given by the triangular area ABC and the Y Axis in the first quadrant. The Base will exist on the Y Axis from Points A to C
The height will be given by the perpendicular distance between the 2 parallel lines of the Y Axis and Vertical Line of X = 6
Further, the rest of the Area of Quadrilateral AECD will be given by the Triangular region in quadrant 1 defined by Point E on line x = 6 and the Base AC located on the Y Axis.
Thus, both triangular regions ABC and AEC will share the common Base on the Y Axis from points A to C and both have their 3rd point on the Parallel Line X = 6:
Point B will be at (6 , 0)
And
Point E will be somewhere between (6 , 20) and (6 , -12)
Because no matter where you put point E on the parallel line X = 6 the perpendicular height between the Y Axis and X = 6 will remain the same, both triangular areas will have the same base and the same height and therefore the same area.
C- the quadrilaterals will have the same area
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Can you explain this "Point E will be somewhere between (6 , 20) and (6 , -12)" perhaps with a drawing? I drew it out and I see no way the two quadrilaterals can have the same area unless E is located at (6,0).