MathDB

ABCD

is any convex quadrilateral. Construct a new quadrilateral as follows. Take

A'

so that

A

is the midpoint of

DA'

; similarly,

B'

so that

B

is the midpoint of

AB'

;

C'

so that

C

is the midpoint of

BC'

; and

D'

so that

D

is the midpoint of

CD'

. Show that the area of

A'B'C'D'

is five times the area of

ABCD

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