M and N are the midpoints of the sides of a square. What is the ratio of the area of triangle AMN to the area of the complete square?

Answer 1

Area of a triangle = ( 1 / 2 ) base * heigh

In this case base = heigh = a / 2

A = ( 1 / 2 ) * ( a / 2 ) * ( a / 2 )

A = a ^ 2 / 8

Area of a square = a ^ 2

( a ^ 2 / 8 ) / a ^ 2 = 1 / 8