Question

Note that the apothem shown is equal to 2 square root of three.

Answer 1

All of the triangles in the figure below are congruent. What is the area of the figure? Note that all measurements are in centimeters.

Answer 2

@jim_thompson5910 help meh

Answer 3

All triangles are congruent. So that 4 that is the base of that upper right triangle is also the base of the top most triangle. Do you see this?

Answer 4

yes i so but my possible answers are weird :(

Answer 5

do*

Answer 6

What are your possible answers?

Answer 7

48 + 24 square root of three.

24 square root of three.

48 square root of three.

24 + 24 square root of three.

Answer 8

so it looks like you want the area of the hexagon as well?

Answer 9

those are my anwsers???

Answer 10

Let's find the area of each triangle and ignore the hexagon for now

Answer 11

So what is the area of that top most triangle?

Answer 12

geez idk 4?

Answer 13

Area:

A = (bh)/2

A = (4*2)/2

A = 8/2

A = 4

So you are correct

Answer 14

There are 6 of these (identical) triangles.


So the total area of the pink area is 6*4 = 24

Answer 15

so which anwser is it?

Answer 16

The hexagon breaks up like so

Answer 17

It's given that the value of h is 2*sqrt(3)

So the area of one triangle in that hexagon is

A = (bh)/2

A = (4*2*sqrt(3))/2

A = 4*sqrt(3)


There are 6 of these triangles, so the area of the hexagon is 6*4*sqrt(3) = 24*sqrt(3)

Answer 18

Finally, add up the two areas we found to get

\[\Large 24+24\sqrt{3}\]

Answer 19

so its the 3rd one?

Answer 20

no

Answer 21

looks like the 4th