Question

Triangle UVW is the pre-image of triangle RST with a scale factor of 3. Find the area of triangle UVW if the area of triangle RST is 9 cm2.


81 cm2

27 cm2

18 cm2

9 cm2

Answer 1

the triangle

Answer 2

An intuitive way to think about this is that area is the square of distance. So, when you scale the distances of the sides by 3, the area scales by 9. So, 9 cm2 becomes 81 cm2.

Answer 3

wow that was simple O_O

Answer 4

I have some similar questions. Think you can have a look?

Answer 5

Absolutely

Answer 6

Quadrilateral HIJK is the pre-image of quadrilateral LMNO. Find the scale factor, t.

Answer 7

the options are 9/4 , 5/3, 9/25, 3/2

Answer 8

So, 375/135 = 2.77ish. You know from the last question that that's the square of the scale factor. Square root it and you get 1.66ish. So, 5/3.

Answer 9

okay i have another I'm just working out what you said so i can have it for myself

Answer 10

Okay, let me know if you have any questions.

Answer 11

Find WZ if the area of trapezoid ABCD is 225 cm2, the area of trapezoid WXYZ is 81 cm2, and AD is 35 cm.

Answer 12

21 cm

12.6 cm

58.3 cm

97.2 cm

Answer 13

So, find the scale factor first, like I did in the last question.

Answer 14

okay :D

Answer 15

2.77

Answer 16

Not quite, you forgot to take the square root.

Answer 17

find the sqrt of 2.77?

Answer 18

Right, 225/81=2.77, but that's the ratio of the areas. To turn that into the ratio of lengths, you need the square root.

Answer 19

the sqrt is 1.66

Answer 20

Right, so now use that to find WZ.

Answer 21

how?

Answer 22

AB/WZ = 1.66

Answer 23

35/21 =1.66

Answer 24

Right, so WZ = 21. Good job!

Answer 25

:D sweet 2 more questions

Answer 26

Find the area of the pre-image rectangle QRST if the area of the image rectangle DEFG is 54 cm^2 and the scale factor is 3/2

Answer 27

216 cm^2

108 cm^2

54 cm^2

24 cm^2

Answer 28

Well, with those choices, it's pretty obvious. It has to be less than 54. But still, try and work it out.

Answer 29

okay :D what is the first step?

Answer 30

Square the scale factor,s ince you're working with area.

Answer 31

2.25

Answer 32

Right. Now, you're going from post image to pre-image, so you have to divide by that.

Answer 33

oh okay

Answer 34

so square 54?

Answer 35

2916

Answer 36

wait oops my mistake

Answer 37

Are you doing 54/2.25?

Answer 38

sorry no i divded 54 and 3/2

Answer 39

You need to divide by the squared ratio, since you're dealing with area.

Answer 40

alright i got 24

Answer 41

Yup, nice job

Answer 42

ty for all your help I am done :D

Answer 43

Great, no problem