Question

Picture in the comments and please help
Find the area if the figure to the nearest hundredth of a centimeter.

Answer 1

@jim_thompson5910

Answer 2

you can break up the hexagon into 6 triangles like this

Answer 3

each triangle is an equilateral triangle with side 1.5

Answer 4

are you able to find the area of each triangle?

Answer 5

Yes? Do times or add 1.5 together? or??

Answer 6

Area of Equilateral Triangle
\[\Large A = \frac{\sqrt{3}}{4}*s^2\]
A = area
s = side length

Answer 7

A is unknown, s = 1.5

Answer 8

Where do I go from there?

Answer 9

what area did you get?

Answer 10

2.25 ? @jim_thompson5910

Answer 11

1.5^2 = 2.25

now multiply that by the square root of 3 over 4

Answer 12

\[\Large A = \frac{\sqrt{3}}{4}*s^2\]
\[\Large A = \frac{\sqrt{3}}{4}*1.5^2\]
\[\Large A = \frac{\sqrt{3}}{4}*2.25\]
\[\Large A = ???\]

Answer 13

5.1? I don't have a calculator with the square root symbol @jim_thompson5910

Answer 14

use this

http://web2.0calc.com/

for square roots, you need to type in `sqrt`

example: type in `sqrt(7)` to mean \(\Large \sqrt{7}\)

Answer 15

so in your case, you'll type in `sqrt(3)/4*2.25`

Answer 16

1.7?

Answer 17

@jim_thompson5910

Answer 18

I'm getting 0.9742785792574935

Answer 19

the area of ONE triangle is 0.9742785792574935

but there are 6 of these triangles total

Answer 20

can't we round that to 10? and wouldn't it be 10*6?

Answer 21

0.97 wouldn't round to 10

Answer 22

I think you mean 1.00?

Answer 23

I wouldn't round just yet

Answer 24

0.9742785792574935*6 = ???

use the calculator. Type in `0.9742785792574935*6` or copy/paste it in

Answer 25

5.845671476

Answer 26

@jim_thompson5910

Answer 27

good

Answer 28

so that takes care of the hexagon portion

Answer 29

now focus on the semicircle portion in blue

see attached

Answer 30

what is the area of that blue semicircle?

Answer 31

8.768507213?

Answer 32

what did you type in to get that?

Answer 33

my answer up top times 1.5

Answer 34

the semi-circle has a radius of 1.5/2 = 0.75


use the area of a semi-circle formula

\[\Large A = \frac{\pi*r^2}{2}\]

Answer 35

0.883572934 thats what my calculator says

Answer 36

mine too

Answer 37

Yayyyyyyy!!!!!

Answer 38

area of hexagon = 5.845671476

area of semicircle = 0.883572934

add the two areas to get the overall figure area

Answer 39

A= 6.72924441

Answer 40

@jim_thompson5910

Answer 41

For part C it says suppose each side length was multiplied by 3. What would be the area of the new figure?

Answer 42

@jim_thompson5910

Answer 43

`each side length was multiplied by 3`
so the new area would be 9 times larger

3^2 = 3*3 = 9

new area = 9*(old area)

Answer 44

Okay, so it would be 9* 6.72924441= 60.56319969

Answer 45

yes

Answer 46

Yayy! Thank you!

Answer 47

yw