For an equilateral triangle, all sides are of equal length.
The area for an equilateral triangle is Area = the square root of 3. divided by 4 and multiplied by the square of the length of a side.
So if you double a side, then the Area is changed by a factor of the original length.
For example, if a side was 2 units long, the area would be doubled. (4 vs 2).
If a side was 3 units long, the area would be tripled (9 vs 3).
As length increases, the area increases by the square of the increase.
If you double the length of the sides of a square, the area increases to 4 times the original area.
If you triple the side length, the area becomes 9 times the original area.
This is true of all polygons and all shapes in general. If you increase a circle so its circumference is 2 times the original the area is 4 times the original area.
So if you increase the sides of a triangle by a factor of 2 the area will increase by a factor of 4.
Area of similar triangles is the ratio of the square of the ratio of their sides.
If each side of an equilateral triangle was doubled, then its area becomes 2² i.e. 4 times
Area = (√3/ 4) s^2 , where ‘s’ is the side
replace s by 2s
Area = (√3/4) (2s)^2 = (√3/4) 4 s^2
= √3 s^2
√3 s^2 is four times (√3/4) s^2
Therefore, the area is quadrupled.