Question

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.

Answer 1

12 unit²

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