Respuesta :

wolf1728
If the sides are in the ratio of 5:3 then the area will increase by a factor of:(5 / 3) ^2
(5 / 3)^2 = 2.777777777
Area of small hexagon = 81
Area of larger hexagon = 81 * 2.777777777
Area of larger hexagon = 225 square meters

lhannearaujo

The area of the larger hexagon is equal to 225 m².

Ratios

Ratios can represent a relation between two sides of a  polygon. When the ratio is greater than 1, it means that the ratio is written as a fraction between the side of the greater polygon and the side of the smaller polygon. Otherwise, if the ratio is less than 1, it means that the ratio is written as a fraction between the side of the smaller polygon and the side of the greater polygon.

Here, it is important that you know: The ratio of the area is equal to the square of the ratio of sides (ratio of areas = (ratio of sides)²).

The question gives:

  • ratio of sides =  3:5
  • area of smaller hexagon= 81 m² .

Like the ratio < 1, you can write the following fraction:   [tex]\frac{smaller\; side}{greater\; side} =\frac{3}{5}[/tex].

As ratio of areas is equal to (ratio of sides)², you can write:

                            [tex]ratio\;of\;area=(\frac{3}{5} )^2\\ \\ ratio\;of\;area=\frac{9}{25} =\frac{smaller\; area}{greater\; area} \\ \\ ratio\;of\;area=\frac{9}{25} =\frac{81}{x}\\ \\ 9x=81*25\\ \\ 9x=2025\\ \\ x=\frac{2025}{9}\\ \\ x=225[/tex]

Read more about ratio of areas here:

https://brainly.com/question/1580563

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