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?
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