# Geometry

Problem:
ABCD is a kite such that AB=BC and CD=DA. P is the centroid of triangle ABC and Q is the centroid of triangle CDA. We know [ABCD]=60. Find [PCQA].

I have no idea on how to approach this problem!

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1. What does [ABCD] represent?
If it is the area of the kite,
then
we know that the area of a kite is the product of the diagonals รท 2.

Note: You are fully expected to draw a duly labelled sketch in order to follow the following explanations.

So AC*BD/2=60
AC*BD=60*2=120

But since centroids are located at 1/3 of the median from the base, so
QP=(1/3)AC
Area of kite PCQA
=PQ*AC/2=(1/3)BD*AC/2=60/3=20

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posted by MathMate

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