Measuring GDP

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I’m looking at Reading 17 Exhibit 1 diagram about the simple economy and its circular flow.
I can see 4 elements - inputs, outputs, income and expenses.
In section 2.1 GDP, it proceeds to say that GDP can be calculated only in two ways - based on outputs and inputs.
Why are expenses and income not used to calculate GDP as well? All of these would equal obviously, but why is there only two ways to calculate GDP?
 
My copy of the 2019 curriculum shows Exhibit 1 mentioning output, income, and expenditure; it doesn’t mention inputs.
It mentions that GDP can be measured using either:
  • The income approach
  • The expenditures approach
and that the expenditures approach has two subapproaches:
  • Value of final output
  • Total value added
 
The reason I ask is because obviously in the two factor model, there are 4 arrows (Income, Expenditure, ‘Labour and Capital’ and ‘Goods and Services’) and it got me thinking, why GDP was measured only using the income and expenditure approaches if there are 4 elements which would imply that we could measure these flows in 4 ways.
Thinking about it some more, I think that Income measures ‘Labor and Capital’ and Expenditure measures ‘Goods and Services’. So there really are only two things that need measurement, ‘Labour and Capital’ and ‘Goods and Services’ and the way to measure those is through Income and Expenditure respectively. At least that’s my thinking.
 
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