Question

Six equilateral triangles are connected to create a regular hexagon. The area of the hexagon is 24a^2 – 18 square units. Which is an equivalent expression for the area of the hexagon based on the area of a triangle?

Answer 1

Help me! Im being timed!!! I failed twice already and this is my last chance!!

Answer 2

what are the options

Answer 3

hold on give me a second

Answer 4

aight

Answer 5

A. 6(4a2 – 3)
B. 6(8a2 – 9)
C. 6a(12a – 9)
D. 6a(18a – 12)
Here they are

Answer 6

your figure will look something like this

Answer 7

i dont have a figure i just have those options that I gave you. They re just numbers no figures

Answer 8

you can make this figure from the given information (:

Answer 9

it has 6 equilateral triangles, all having the same area because they have the same side length which is equal to the side length of the hexagon

Answer 10

what does it mean? Like from the options I have given you, which would you say fits best?

Answer 11

do you know how to multiply?

Answer 12

yes

Answer 13

\(\color{#0cbb34}{\text{Originally Posted by}}\) @RyeBread1
A. 6(4a2 – 3)
B. 6(8a2 – 9)
C. 6a(12a – 9)
D. 6a(18a – 12)
Here they are
\(\color{#0cbb34}{\text{End of Quote}}\)
you could just multiply and expand the options to see which one matches with the given area of the hexagon, that'll be your answer

Answer 14

not the best approach but it works in this case.

Answer 15

what am i multiplying

Answer 16

lol

Answer 17

the things inside the parentheses with the things outside the parentheses...
for example option B-

\(6(8a^2 -9) = 6*8a^2 -9*6 \\~~~~~~~~~~~~~~~~~~~= 48a^2 - 54\)

Answer 18

ok so i just have to subtract 48a ^2 by 54?

Answer 19

no lol

Answer 20

oh

Answer 21

What do you get when you multiply and expand option A?

Answer 22

i dont know because i dont understand what expand means. i know i sound really dumb but i honestly have no idea how to do this

Answer 23

aight i'll walk you through

Answer 24

\(\color{#0cbb34}{\text{Originally Posted by}}\) @imqwerty
the things inside the parentheses with the things outside the parentheses...
for example option B-

\(6(8a^2 -9) = 6*8a^2 -9*6 \\~~~~~~~~~~~~~~~~~~~= 48a^2 - 54\)
\(\color{#0cbb34}{\text{End of Quote}}\)
do you understand how i opened the parantheses here?

Answer 25

thanks

Answer 26

yeah you used the distributive property

Answer 27

yeah, that's what i mean when i say 'expand'

so try using the distributive property on option A

Answer 28

ohh ok

Answer 29

tell me what you get

Answer 30

ok

Answer 31

24a^2-3

Answer 32

is that right

Answer 33

the first term (24a^2) is correct but not the second term (3)

Answer 34

what am i supposed to do to term 3

Answer 35

you didn't use the distributive property correctly. Check this image above and try using the distributive property again on option A

Answer 36

is it supposed to be 24a^2-18

Answer 37

yes

Answer 38

haha im so smart i got it right and thats the right answer

Answer 39

Thanks so much!

Answer 40

yw

Answer 41

checking the options using distributive property worked in this case because of weak options

imagine an option E) 2(12a^2 - 9)

It gives the same result: 24a^2 -18 when you use the distributive property but it's not correct because the expression 2(12a^2 -9) is not based on the area of triangle

Answer 42

ohhh very true i get these type of ?s now!

Answer 43

there are 6 triangles each having an equal area. So you could just multiply the area of one triangle with 6 to get the area of the hexagon.

so your expression should be of type: \(6 \times (Area~of~one~triangle)\)

it has to have a 6 and a quadrative term(the expression for the area of the triangle is a quadratic term) and the entire expression should also simplify to the area of the hexagon. The option follows this is correct.

Answer 44

thanks for the help because i wouldnt have gotten a good score if i hadnt posted that question. I got an 80% just so you know

Answer 45

That's nice :) yw