Question

If each side of a triangle is halved the area will be decreased by

Answer 1

By Heron's formula the area will decrease by 75%

Answer 2

For a triangle with sides a, b, and c,

we get semi-perimeter =s=a+b+c/2

by Heron’s formula,

Area =Δ=√(s)(s−a)(s−b)(s−c)

Now, consider another triangle with sides a/2, b/2 and c/2.

Now, the semi-perimeter =s′=(a+b+c)/4=s/2.

by Heron’s formula,

Area=Δ′=√(s)(s−a)(s−b)(s−c)/16=Δ4.

Therefore, the change in area is 75%.