The vertices of a quadrilateral ABCD are A(4,8) B (10,10) C (10,4) and D ( 4,4). The vertices of another quadrilateral EFCD are E(4,0) F (10,-2), C( 10,4) and D ( 4,4). Which conclusion is true about the quadrilaterals?

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

true

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