The Midpoints of Two Cevians

area(AMN)

≈

17.57

4area(AMN)

≈

70.27

area(BC'B'C)

≈

70.27

A cevian is a line drawn from a vertex of a triangle to the opposite side.

Let ABC be a triangle and let M and N be the midpoints of the cevians BB' and CC'. Then the area of the quadrilateral BC'B'C is 4 times the area of AMN.