QUESTION 6
Easy
ABCD is a parallelogram. P and Q are any two points on side AB. What can you say about the ratio area (ΔPCD) : area (ΔQCD)?
SOLUTION
For point P on AB,
\(Area(ΔPCD) = \frac{1}{2} \, × \,CD \,×\, h\),
where \(h\) is the perpendicular distance between the parallel lines AB and CD.
Similarly, for point Q on AB,
\(Area(ΔQCD) = \frac{1}{2} \, × \,CD \,×\, h\)
Thus, the two areas are equal. The ratio is 1:1.
\(Area(ΔPCD) = \frac{1}{2} \, × \,CD \,×\, h\),
where \(h\) is the perpendicular distance between the parallel lines AB and CD.
Similarly, for point Q on AB,
\(Area(ΔQCD) = \frac{1}{2} \, × \,CD \,×\, h\)
Thus, the two areas are equal. The ratio is 1:1.
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Final Answer : The ratio of the areas is 1:1
Concept Note
The area of a triangle if given by the formula
<\Area = \frac{1}{2} \,× \,base\,×\,height\>
In a parallelogram, the base CD is fixed, and the height from any point on side AB to line CD is constant because AB is parallel to CD.