Asked by Lali
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!
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!
Answers
Answered by
MathMate
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 ÷ 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
If it is the area of the kite,
then
we know that the area of a kite is the product of the diagonals ÷ 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