Lot of mathematicians have proved Pythagoras theorem in their own ways. If you google it you will indeed found hundred of ways.

Meanwhile I was also sure that maybe one day I could find something new out of this incredible Pythagoras theorem and Recently I got something which I would like to share with you.

To Prove: Deriving the equation of area of trapezium using Arcs

Proof: There is a triangle ABC with sides a b and c as shown in the figure.

Now,

Area of ∆ BCEG = Area of ∆ BDC +Area of ⌂ DCEF + Area of ∆ EFG c^2=ac/2+ Area of ⌂ DCEF + (c-b) c/2 (2c^2– ac –c^2+ bc )/2=Area of ⌂ DCEF (c^2– ac+ bc )/2=Area of ⌂ DCEF c(c– a+ b)/2=Area of ⌂ DCEF Area of ⌂ DCEF=BC(DE+CF)/2

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