Suppose abcd is a convex quadrilateral. points m and n are midpoints of sides bc and ad, respectively. the area of the quadrilateral amcn is equal to 6 square units. find the area of quadrilateral abcd.

12 unit²

Step-by-step explanation:

area ΔAMC = 1/2 CM x AH' = 1/4 BC x AH'

area ΔABM = 1/2 BM x AH' = 1/4 BC x AH'

area ΔAMC = area ΔABM

for the same calculation, we can prove

area ΔACN = area ΔDCN

area ΔAMC + area ΔACN = 6

area ΔABM + area ΔDCN = 6

ABCD = area ΔAMC + area ΔACN + area ΔABM + area ΔDCN = 6 = 6 = 12

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