Answer:
8 ft²
Step-by-step explanation:
Since ΔEFG ~ ΔABC, they are proportionately related. Each of the corresponding sides differ by the scale factor, which shows how much bigger or smaller the new triangle is from the original triangle.
Purple = original triangle, triangle 1
Pink = new triangle, triangle 2
Find the scale factor, "k". It will be a fraction because the triangle gets smaller.
k = FG/BC = 2/3
The scale factor can be used to find a side, the height or the area of the new triangle.
Use the scale factor squared to find the area.
A₂ = (A₁)(k²)
= (18 ft²)(2/3)²
= 7.999...ft²
= 8 ft²
