what is the answer to this pls

Problem:

ABCD is a kite such that AB=CD and CD=DA. P is the centroid of triangleABC and Q and is the centroid of triangleCDA. We know [ABCD]=60. Find [PCQA]

saisagod Jan 18, 2019

#1**+1 **

If CD = DA, then AB = BC [ not AB = CD ] since a kite has two distinct [different ] pairs of equal adjacent sides

[If AB = CD, we would have a square or a rhombus ]

Let the diagonals be AC and BD

And let their intersection = E

Since P is a centroid, then EP = 1/3 of EB

And similarly, EQ = 1/3 of ED

So.....the area of the kite = AC * EB / 2 + AC * ED / 2 = (1/2) [ AC * EB + AC * ED ]

And the area of triangle ABC = AC * (1/3)EB / 2 = AC * EB / 6

And the area of triangle ADC = AC * (1/3)ED / 2 = AC * EB / 6

So...the area of PCQA = area of triangle ABC + area of triangle ADC = (1/6) [ AC * EB + AC * ED] =

(1/3) (1/2) [ AC * EB + AC * ED ] =

(1/3) area of kite = 20

CPhill Jan 18, 2019