Question 1078916


 By definition, two polygons are similar if and only if their corresponding angles are congruent and there is a proportional relationship among the measures of the corresponding sides. 

if corresponding sides {{{AB=6in}}} and {{{A}}}'{{{B}}}' ={{{9in}}} and the large polygon has area {{{A=20.25in^2}}}, than the area of the small polygon {{{A}}}' will be:

{{{A}}}:{{{A}}}' ={{{AB}}}:{{{A}}}'{{{B}}}'

{{{20.25in^2}}}:{{{A}}}'={{{6in:9in}}}

{{{A}}}'*{{{9in}}}={{{6in*20.25in^2}}}

{{{A}}}'*{{{9in}}}={{{121.5in^3}}}

{{{A}}}'={{{121.5in^3/9in}}}

{{{A}}}'={{{13.5in^2}}}