6th Grader Equilateral triangles finding the Area

I

ICPassionfruit

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My daughter is in need of help if someone can help her to understand how to get the answer.

Thanks

Q: The area of equilateral triangle ABC is 12 cm2. What is the area of equilateral triangle DEF if the sides are two times as long as the sides of triangle ABC? Explain your Answer.
 
ICPassionfruit said:
Q: The area of equilateral triangle ABC is 12 cm2. What is the area of equilateral triangle DEF if the sides are two times as long as the sides of triangle ABC? Explain your Answer.
Click to expand...
If s is the lenght of a side of an equilateral triangle then its area is \(\displaystyle \frac{\sqrt3 s^2}{4}\).
Now replace s with 2s.
 
hopefully she will understand your reply ty if not I will check back. I have been out of school to long to remember some of the math. lolo
 
ICPassionfruit said:
My daughter is in need of help if someone can help her to understand how to get the answer.
Click to expand...
Why can't she ask herself?
 
ICPassionfruit said:
My daughter is in need of help if someone can help her to understand how to get the answer.

Thanks

Q: The area of equilateral triangle ABC is 12 cm2. What is the area of equilateral triangle DEF if the sides are two times as long as the sides of triangle ABC? Explain your Answer.
Click to expand...

There's MUCH I don't know about what your daughter has studied, so I'm guessing at what she may (or may NOT) understand.

First of all, I assume she may be studying similar figures. ANY two equilateral triangles are similar...same shape.

Secondly, the AREAS of two similar figures have a ratio that is the square of the ratio of any pair of corresponding sides.

You are given two equilateral triangles, ABC and DEF. You are told that the sides of triangle DEF are two times as long as the sides of triangle ABC, so the ratio of one side of triangle ABC to the corresponding side of triangle DEF is 1/2.

If the ratio of a pair of corresponding sides is 1/2, then the ratio of the areas is (1/2)^2, or (1/2)*(1/2), or 1/4

So,

area of triangle ABC = (1/4)*area of triangle DEF

12 = (1/4) * area of triangle DEF

Can you take it from here?
 
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