Question

Two regular pentagons have perimeters of 8cm and 16cm. What is the ratio of their areas?

Answer 1

1:2

Answer 2

no

Answer 3

perimeter is a linear measure, the scale factor would be 1:2

however, you'd have to square these numbers to get the scale factor for the areas

Answer 4

i don't quite understand sorry

Answer 5

let's look at something simple, like a square.



do you see one of the inside squares? the outside square has twice the length. but how many time the area?

Answer 6

4?

Answer 7

yep, \(4=2^2\)

Answer 8

is it 8^2 / 16^2 ? which equals to 4

Answer 9

same for circles, too.

if a smaller circle has a radius of 3, it will have an area of \(\pi r^2 = 9\pi\)

if you double the radius to 6, the area is now \(\pi r^2 = 36\pi\) which is 4 times more.

Answer 10

Oh ok I see now. I didn't know it asked for area

Answer 11

that works.

if \(P_1:P_2 = 1:2 \Rightarrow P_1^2:P_2^2 = 1^2:2^2 = 1:4\) the P is the perimeter, a linear measure.

for volumes, you have to cube the linear scale factor.

Answer 12

you good?

Answer 13

i do understand a bit but how does that get me the ratio of areas ?

Answer 14

how did you know the perimeter of p1 and p2 is 1:2

Answer 15

it's given... 8:16 = 1:2

Answer 16

OHH ok because they both are multiples of 8 sorry im quite slow at this haha

Answer 17

also, \(8:16=\Large{\frac{8}{16}}\normalsize{=}\Large{\frac{1}{2}}\)

Answer 18

you got it!

Answer 19

is 1:2 the finally anwser ?

Answer 20

no... you have to square those numbers to getthe ratio of the areas. the 1:2 is for their perimeters (a linear measure)

Answer 21

If it was a line you would be using 1:2
but because it is area that they are asking for you have to square it \[1^2:2^2\]

Answer 22

@pgpilot326 am I right?

Answer 23

yes

Answer 24

so 1:4 ?

Answer 25

you got it!

Answer 26

thankds !

Answer 27

you're welcome!