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? But the answer has to be in a ratio which is the area of a triangle to the area of the complete square. Also the triangle is in the square at top corner.

Answer 1

Let x = length of side of square
thus area of square is
A,square = x^2
recall that area of triangle is given by
A,triangle = (1/2)b*h
where b is the base and h is the height.
The base and height of the triangle AMN are equal, which is (1/2)x. Thus,
A,triangle = (1/2)*[(1/2)x]*[(1/2)x]
A,triangle = (1/8)x^2

Getting the ratio of areas,
A,triangle : A,square = (1/8)x^2 : x^2 = 1/8

hope this helps~ :)