Find the area of the quadrilateral - 1

Geometry Level pending

In quadrilateral A B C D ABCD shown above, A C = B D AC=BD . Points W , X , Y W,X,Y and Z Z are the midpoints of A B , B C , C D AB,BC,CD and D A DA , respectively. If W Y = 4 WY=4 and Z X = 9 ZX=9 , find the area of quadrilateral A B C D ABCD .

36 18 48 24

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Since it is an equidiagonal quadrilateral, the area is the product of the bimedians. We have

A A B C D = ( W Y ) ( Z X ) = 4 ( 9 ) = A_{ABCD}=(WY)(ZX)=4(9)= 36 \boxed{36}

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