Find the ratio of the areas.

9514 1404 393

  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

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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.

1) 420mm

2) 837grams

3) 0.89litres

4) 0.072

5) 0.00267

Step-by-step explanation:

1) divide by 10

2) multiply by 1000

3) divide by 1000

4) divide by 1000

5) divide by 10,000