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I'm not very confident in this answer, but here goes! My answer may be a little TOO simple, because I think that the area should be 18cm squared. How I got this? I multiplied 6 (triangle ABC's area) by 3, because I know all the side lengths of triangle DEF are 3 times of ABC. Just to make sure I was correct, I worked backwards. To find the area of a triangle, it's obviously bxh/2, so if 6 is my area, the base and height of my triangle is 12. If let's say, the base was 2 and height was 10, then triangle DEF's base would be 6, and 30 for the height. Together, it's 36, 3 times the amount of 12. If I switch around the numbers, like 1 and 11 for example, the end result is still 36. 36/2 is 18, which is also 3 times triangle ABC's area, and that's how I know triangle DEF's area should be 18 cm squared.
Also, I found that the second part of the paragraph (explaining similarity) didn't really help/apply to this question. Is that section for people who needed a reminder of similar shapes? In fact, it confused me a little because I thought I needed to incorporate that somehow to get the answer.
Anywho, thanks for reading if you made it this far. ;)
That`s me... Again It says it`s MY ACCOUNT (Emily Du), but shows up as my sisters...... Strange. But it`s not on purpouse!!!!! (Mr.Milette, this is the fourth in a row, I deserve another candy!!!! :D)
NOW TO SOLVE THIS QUESTION: LETS PRETEND THAT TRIANGLE ABC HAS SIDE LENGTHS 6,2,AND ANYTHING, WHERE DE IS 2, EF IS 6, AND DF CAN BE ANYTHING. SINCE 6*2=12 AND 12/2 = 6, THE INFORMATION IS ACCURATE. 2*3= 6, 6*3= 18. 6*18=108. 108/2=54. THE NEW AREA IS 54CM2.
We think that the area of Triangle DEF is 54 cm2. Here is how we got the answer:
We know that the area of Triangle ABC is 6. If we multiply 6 by 2 (because of the formula bxh/2), we get 12. This means that the variables/factors b and h must produce a product of 12. We assumed that the lengths of AB and BC were 2 and 6.
6 (base) x 2 (height) = 12 12/2 = 6 6 = Area of Triangle ABC
Now that we have the lengths of AB and BC, we multiplied each value by 3. 6x3=18 2x3=6
Great work y'all. I like how you used your knowledge of corresponding angles, side lengths, and other triangle relationships to show your work. Yes, the correct answer was 54cm squared.
And yeah, I screwed something up in my process.... Weird... If it's 2 and 10, it's 24 as the area, so that was my fault again! Whoopsies. I guess I sorta replaced multiplication with addition. OH NO ;A; So if you don't mind me re-explaining in here, if it was 2 and 6 as the basexheight (numbers that actually MAKE 12), 2x3=6. and 6x3=18, and 18x6/2 is 54, so I understand now. Thanks for the correction Jonathan!
I'm not very confident in this answer, but here goes!
ReplyDeleteMy answer may be a little TOO simple, because I think that the area should be 18cm squared.
How I got this? I multiplied 6 (triangle ABC's area) by 3, because I know all the side lengths of triangle DEF are 3 times of ABC.
Just to make sure I was correct, I worked backwards. To find the area of a triangle, it's obviously bxh/2, so if 6 is my area, the base and height of my triangle is 12. If let's say, the base was 2 and height was 10, then triangle DEF's base would be 6, and 30 for the height. Together, it's 36, 3 times the amount of 12. If I switch around the numbers, like 1 and 11 for example, the end result is still 36. 36/2 is 18, which is also 3 times triangle ABC's area, and that's how I know triangle DEF's area should be 18 cm squared.
Also, I found that the second part of the paragraph (explaining similarity) didn't really help/apply to this question. Is that section for people who needed a reminder of similar shapes? In fact, it confused me a little because I thought I needed to incorporate that somehow to get the answer.
Anywho, thanks for reading if you made it this far. ;)
Hi Emily. Correct me if I'm wrong but I noticed something in your statement.
Delete"If let's say, the base was 2 and height was 10, then triangle DEF's base would be 6, and 30 for the height. Together, it's 36,"
I agree that the base would be 6 and 30, but does it actually become "36"?
6x30 = ?
My gosh, I was wrong again....
DeleteWhoops
I see the fault in my answer
I feel so embarrassed now, hehe... I'm on a losing streak man.....
That`s me... Again
ReplyDeleteIt says it`s MY ACCOUNT (Emily Du), but shows up as my sisters...... Strange. But it`s not on purpouse!!!!!
(Mr.Milette, this is the fourth in a row, I deserve another candy!!!! :D)
I know it's you. And "deserve"? How about "I think I've earned..." hehe
DeleteNOW TO SOLVE THIS QUESTION: LETS PRETEND THAT TRIANGLE ABC HAS SIDE LENGTHS 6,2,AND ANYTHING, WHERE DE IS 2, EF IS 6, AND DF CAN BE ANYTHING. SINCE 6*2=12 AND 12/2 = 6, THE INFORMATION IS ACCURATE. 2*3= 6, 6*3= 18. 6*18=108. 108/2=54. THE NEW AREA IS 54CM2.
ReplyDeleteMy sister and I did this together
ReplyDeleteWe think that the area of Triangle DEF is 54 cm2. Here is how we got the answer:
We know that the area of Triangle ABC is 6. If we multiply 6 by 2 (because of the formula bxh/2), we get 12. This means that the variables/factors b and h must produce a product of 12. We assumed that the lengths of AB and BC were 2 and 6.
6 (base) x 2 (height) = 12
12/2 = 6
6 = Area of Triangle ABC
Now that we have the lengths of AB and BC, we multiplied each value by 3.
6x3=18
2x3=6
18 (base) x 6 (height) = 108
108/2 = 54
Therefore, the area of Triangle DEF is 54 cm2
Great work y'all. I like how you used your knowledge of corresponding angles, side lengths, and other triangle relationships to show your work. Yes, the correct answer was 54cm squared.
ReplyDeleteAnd yeah, I screwed something up in my process.... Weird...
ReplyDeleteIf it's 2 and 10, it's 24 as the area, so that was my fault again! Whoopsies. I guess I sorta replaced multiplication with addition. OH NO ;A;
So if you don't mind me re-explaining in here, if it was 2 and 6 as the basexheight (numbers that actually MAKE 12), 2x3=6. and 6x3=18, and 18x6/2 is 54, so I understand now.
Thanks for the correction Jonathan!