Freddy has a triangular flag. He wants to cut out a similar flag that has dimensions one-third of the original flag. If the area of the original flag is 108 square inches, what is the area of the new flag that Freddy cuts out?

12 in2

36 in2

18 in2

40 in2

Question

Freddy has a triangular flag. He wants to cut out a similar flag that has dimensions one-third of the original flag. If the area of the original flag is 108 square inches, what is the area of the new flag that Freddy cuts out?

 12 in2

 36 in2

 18 in2

 40 in2

directrix · Answer

12 in2
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The two flags are similar with a one to three scale factor from small flag to large flag.

If two plane figures are similar, the square of the scale factor is the ratio of the areas.

1/9 = x/108 where x is the area of the new and smaller flag
9x = 108
x = 12 square inches