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ATQ, If the sides of a triangle are all doubled, the area of the triangle increases by a factor of 4. Let A be the original area of the triangle with sides a, b and c. The Semiperimeter (s) is given as {s = (a+b+c)/2} The original area 'A' is given by Heron's formula: 
Now if we double all the sides, the new sides are 2a, 2b and 2c , and the new Semiperimeter (s') is {s' = (2a +2b+2c)/2} = 2s The new area A′ is given by Heron's formula with the new sides: 
Now, let's compare A′ with A: 
Therefore, doubling the sides of a triangle results in an area that is 4 times larger.
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