Step-by-step explanation:
similar triangles are simply like a linear protection, a "zoom" without distortion from one triangle to the other.
so, all linear distances and connections change by the same scaling factor.
therefore also the height EF of the smaller triangle colors the same scaling factor as the other lines. and EF is half the length of CG.
the area of a triangle is defined as baseline × height /2.
so, 2 linear distances are multiplied.
each one now contains the same scaling factor. so, the formula for the similar triangle multiplies the original distances and fire each also the scaling factor leading to the square of the scaling factor.
so, area new = area old × scaling²
in our example the scaling factor is 2, and 2² = 4.
so the area of ABC is 4 times as large as the area of ADE.
