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A large gazebo is shaped like a regular octagon. it has sides of length 12 feet and an area of 696 square feet. find the area of a smaller gazebo that has a side length of 8 feet.

Respuesta :

Check the picture below.

since they're similar figures

[tex]\cfrac{12^2}{8^2}~~ = ~~\cfrac{696}{A}\implies \cfrac{144}{64}~~ = ~~\cfrac{696}{A}\implies \cfrac{9}{4}=\cfrac{696}{A}\implies 9A=2784 \\\\\\ A=\cfrac{2784}{9}\implies A=\cfrac{928}{3}\implies A=309\frac{1}{3}[/tex]

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