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2 years ago

Find the ratio of the areas.

Mathematics

1 answer:

pshichka [43]2 years ago

3 0

9514 1404 393

Answer:

3 -2√2

Step-by-step explanation:

For a regular octagon of side length s, the "flat-to-flat" dimension across the center is s(1+√2). The flat-to-flat dimension of the shaded center octagon is simply s. The ratio of areas is the square of the ratio of linear dimensions, so we have ...

small area / large area = (1/(1+√2))^2 = 1/(3+2√2)

small area/large area = 3 -2√2

_____

The attachment shows octagons after the fashion described here. The side length of the larger one is 2 units. The numbers inside are the areas. They have the ratio shown above.

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3 years ago

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