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The sum of the areas of two similar polygons is 65 square units. If their perimeters are 12 units and 18 units, respectively, what is the area of the larger polygon?

 Jan 10, 2020
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Let the area of the smaller polygon be  A

 

The scale  factor  of the larger polygon to  to the smaller polygon  = 18/12 =  3/2

 

So....the  area  of the larger polygon =  (scale factor)^2 * A =   (3/2)^2 * A =   (9/4)A

 

So......we have that

 

A  + (9/4)A   =  65

 

(13/4)A  = 65       multiply both sides by   4/13

 

A =  65 (4/13)  =   20

 

So......the area of the  larger polygon =  (9/4) * 20   =   45

 

 

cool cool cool

 Jan 10, 2020

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