Posted by **alandra** on Saturday, May 19, 2012 at 10:07am.

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.

- math -
**Jai**, Saturday, May 19, 2012 at 11:19am
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~ :)

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