Distance Calculation with different prices

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I've got a problem with the calculation of the delivery price.

The problem is we need to calculate route distance with 2 different prices.

Let's say the distance is 10km .

6km is inside local area(we need to draw by ourselves , polygon) The rest 4km is outside of the scope.

We need to price the first part of the distance say 6km by X price, 4km by Y price.

How can we do the calculation ?

What Google API? And how to use the polygon of Google earth?

I no idea what API to use and how-to use?

So far I've used matrix distance API to calculate to calculate distance between two locations.

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