Answer:
Step-by-step explanation:
Note that refers to the area of some polygon .
Diagonal forms two triangles, and . Both of these triangles have an equal area, and since the area of parallelogram is given as , each triangle must have an area of .
Furthermore, is broken up into two smaller triangles, and . We're given that . Since and represent bases of and respectively and both triangles extend to point , both triangles must have the same height and hence the ratio of the areas of and must be (recall ).
Therefore, the area of each of these triangles is:
With the same concept, the ratio of the areas of and must be respectively, from , and the ratio of the areas of and is also , from .
Let and (refer to the picture attached). We have the following system of equations:
Combine like terms:
Multiply the second equation by , then add both equations: