I need help please and thank you

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How to get this answer

Focus on the top most sides of 4 and 28, which are on the smaller and larger octagons respectively.

The jump from 4 to 28 has us multiply by 7

4*7 = 28

The other sides will follow the same pattern of "multiply by 7"

3*7 = 21

7*7 = 49

6*7 = 42

See the diagram below

After you know all the 7 other sides of the larger octagon, you add them all up

28+28+21+21+49+28+21+42 = 238

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With a lot of math problems, there's often an alternate route which is much faster. In this case, we can multiply the perimeter of the smaller octagon by the scale factor 7 to get the same answer

(smaller perimeter)*(scale factor) = (larger perimeter)

34*7 = 238

so the larger perimeter is 238

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Why does this work? Let's say the sides of the smaller octagon are: a,b,c,d,e,f,g,h

adding up those sides gets us a+b+c+d+e+f+g+h

now imagine multiplying all those sides by the same number 7

a becomes 7a, b becomes 7b, and so on

The new larger perimeter is 7a+7b+7c+7d+7e+7f+7g+7h which we can factor out that 7 and we get 7*(a+b+c+d+e+f+g+h). The stuff inside the parenthesis is exactly the old smaller perimeter we found earlier, so therefore we have

new perimeter = 7*(old perimeter)

215.92 dollars is the answer