Find the area of EFG
EFG = ABC. I need both green box and grey box please .

8 ft^2

(8 in green box; 2 in grey box)

Step-by-step explanation:

We have 2 similar triangles, ABC and EFG.

The area of triangle ABC is given as 18 sq ft.

Side BC of triangle ABC measures 3 ft.

The corresponding side to BC in triangle EFG is FG. It measures 2 ft.

That gives us a scale factor from triangle ABC to triangle EFG.

To find the scale factor between two similar polygons, divide the length of a side of the second polygon by the length of the corresponding side of the first polygon.

scale factor = FG/BC = (2 ft)/(3 ft) = 2/3

The scale factor of side lengths is 2/3.

The ratio of the areas is the square of the scale factor.

ratio of areas = (2/3)^2 = 4/9

Now multiply the area of the first triangle by the ratio of areas to get the area of the second triangle.

area of triangle EFG = (4/9) * (area of triangle ABC)

area of triangle EFG = (4/9) * (18 sq ft)

area of triangle EFG = 8 sq ft

8 ft^2

(8 in green box; 2 in grey box)

a negative exponent is translated as follows:

so, we have