What would new area be?

Question

Given equilateral triangle ABC with sides of length 2. M,N, and P are midpoints of sides BC, AB, and AC, respectively. If A is folded to M,B is folded to P, and C is folded to N, what would the new area be of the folded region?

Answer 1

The area of a triangle is ½bh. The height of the original triangle can be found using Pythagoras: b=√(3)*1 = √3. The area of the original triangle = ½bh = (√(3)*2)*½ = √(3).

 

Since each side of the equilateral triangle was reduced by a factor of two (=1), the new area was reduced by a factor of four and, thus, A= ¼√(3)

Answer 2

After folding, the new area would be the area of the triangle NMP, which is an equilateral triangle with sides of length 1. So its area is sqrt(3)/4.