1997 PMWC Problems/Problem T1
Problem
Let be an equilateral triangle with sides of length three units.
,
,
,
,
, and
divide the sides into lengths of one unit. Find the ratio of the area of the shaded quadrilateral
to the area of the triangle
.
Solution
Triangles UWQ, PUY, UWX, and UXY are all right triangles with side lengths 1, , and 2. Thus
and
.