Answer:
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
Answer: 8 ft^2
(8 in green box; 2 in grey box)
