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For our ancestors who didn’t have the benefit of a world map...

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For our ancestors who didn’t have the benefit of a world map...

Rizom - April,2018
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For our ancestors who didn’t have the benefit of a world map...

Rizom - April,2018
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For our ancestors who didn’t have the benefit of a world map...

Rizom - April,2018
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PK 2017-11-23 02:55
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A New way, The Area of Trapezium

A New way, The Area of Trapezium


Untitled drawing.jpg

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

Copyrighted©PiyushGoel



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