Find the measure please, I got 3 but it's wrong?

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Find the measure please, I got 3 but it's wrong?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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find the measure of what?
D?

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Sorry the area of triangle DEF
ok, so A=12 is the area of the first triangle
Yes. I went by the side of the first and second. The first was 4 and the second was 1 so I thought that the first triangle was 4 times greater than the second. 12/4=3
each side of the triangle on the right is scaled down by a factor of 1/4.
Correct...
Area of a triangle is base*height/2 so,\[\frac{\left| AC \right|4*\sin A}{2}=12\]for the triangle on the left. The triangle on the right is:\[\frac{\left| DF \right|1*\sin D}{2}=?\]Sow the sides AC and DF are related. DF=(1/4)AC and the angles A and D (and therefore their sines) are equal. so, we can write the second equation above as:\[\frac{(1/4)\left| AC \right|1*\sin A}{2}=?\]comparing this with the first equation, we see that 2AC*sinA=12 and (1/8)AC*sinA=?. Now we see that the second equation is 1/16 of the first one. So the area of the second triangle must be 12/16=3/4
So, in summary, if one side of a triangle is scaled by a factor of x, then the area of the second triangle is x^2*area of the first.
where x=1/4 in this example.
Thanks so much!! I got it now!
no prob :)
New fan= me(:
and if you are scaling volumes, it is the same type of argument. Only now you use x^3 instead of x^2 because there is an extra dimension.

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