MathDB

5

Part of 1972 USAMO

Problems(1)

Area of Pentagon

Source: 1972 USAMO Problem 5

3/6/2010
A given convex pentagon ABCDE ABCDE has the property that the area of each of five triangles ABC,BCD,CDE,DEA ABC, BCD, CDE, DEA, and EAB EAB is unity (equal to 1). Show that all pentagons with the above property have the same area, and calculate that area. Show, furthermore, that there are infinitely many non-congruent pentagons having the above area property.
geometryparallelogram