Question

1. Find the area of the regular polygon. Give the answer to the nearest tenth.

pentagon with a side of 6 m (1 point)
123.9 m²
12.4 m²
61.9 m²
49.5 m²

Answer 1

The answer is 61.9m^2, do you need me to show you the steps of how to do it?

Answer 2

Do you know the distance from the center of a side to the center?

Answer 3

yeah thatd be nice

Answer 4

Because the formula for area is,
\[A = \frac{5}{2} s a\]

Answer 5

oooooooo lol okay

Answer 6

That help? You have a pic of the problem that you are working on? Or draw it?

Answer 7

the one i posted after i asked the second question. and i accidently clicked an answer so thats not the answer i picked lol

Answer 8

huh?

Answer 9

this one lol

Answer 10

Well, the minor arc is 50 degrees. You have the point D out to the side. So, to go from A, to D, to B would be 360 degrees for the whole circle minus the part that you don't cover, the 50 degrees.
Did that make sense?

Answer 11

so it would be 310?

Answer 12

so c?

Answer 13

correct!

Answer 14

sweet! lol okay i have more

Answer 15

so would you do 8% of 360?

Answer 16

and id be a??

Answer 17

.08*360

Answer 18

i dont have a calculator on me atm, sorry, but it should be .08*360

Answer 19

and that equals 28.8 lol

Answer 20

alright, then that should be the angle then.

Answer 21

is this d?

Answer 22

Yes, for circumference it is pi times diameter

Answer 23

mkay i got a couple more is that okay?

Answer 24

Ok, on this one, we are looking for 3/4 of the circle. The radius is 6, so the diameter is 12.

Answer 25

okayy

Answer 26

\[C = \pi d\]
In this case we want\[(\frac{3}{4})(C) = (\frac{3}{4})(\pi d)\]

Answer 27

9 pi?

Answer 28

Should be!

Answer 29

yay lol okay

Answer 30

For this one, you are going to want to find the area of the entire circle, and then find the area of the smaller internal circle. Then subtract the smaller circles area from the larger circles area.

Answer 31

thats confusing..

Answer 32

Ok, the diameter for the large circle is 5.4+2.2. The radius is (5.4+2.2)/2.
That is the large circle's radius.
The area of a circle is
\[A = \pi r^2\]
So you would have
\[A_1 = \pi (\frac{5.4+2.2}{2})^2\]
The smaller circles diameter is 5.4, so the radius is 5.4/2.
\[A_2 = \pi (\frac{5.4}{2})^2\]
The area of the decking would be
\[A_{decking} = A_1 - A_2\]

Answer 33

Make any more sense?

Answer 34

kinda

Answer 35

could you calculate the area of the whole circle for me?

Answer 36

i think i got 132.73

Answer 37

or mayby 45.36? idk i suck at math

Answer 38

i got 45.3645979

Answer 39

k lol

Answer 40

then, we need to find the second area

Answer 41

k hold on

Answer 42

22.90?

Answer 43

Correct! Now you need to subtract that value from the value we found before.

Answer 44

22.46

Answer 45

Which when rounded to the tenth is?

Answer 46

d

Answer 47

Um... yeah... somehow we got off by a few tenths.... idk, D should be the correct answer.

Answer 48

okayy lol.. 2 more

Answer 49

Ok, for problem number 9.

We are given an arc of a circle, that is 140 Degrees. We are given the radius.
We can give the area of a circle as
\[A = \pi r^2\]
We want the ratio of 140 degrees to 360 degrees... or in other words 140/360.
Can you find that for me?

Answer 50

umm a=254.5

Answer 51

the other one is 31.5.. would that be the answers?

Answer 52

that is the area of the whole circle. We want just the area in the arc of 140 degrees which is 0.388888889 of the whole circle. So we would take the answer you got, of 254.5 and multiply it by 0.38888889 to get 98.960, or in other words 99.

Answer 53

ohhh okayy lol

Answer 54

On the last one, I am a bit rusty on the geometry... I am thinking of how to solve it right now.

Answer 55

ok lol

Answer 56

We are asked to find the area of a segment. Which is that little shaded sliver of the circle.
First we need to find the height of the triangle.
Are you familiar with the cosine rule?

Answer 57

nope

Answer 58

Ok,
The law of cosines is given as,
\[c^2 = a^2 + b^2 - 2 a b \cos (C)\]

Answer 59

C is my backspace button doesnt work...

Answer 60

wtf...

Answer 61

brb

Answer 62

what? lol

Answer 63

oka y

Answer 64

i can type and it doenst work

Answer 65

Much better!

Answer 66

haha okay

Answer 67

ok, so c is the straight line that is across the segment of the circle, and C is 120 degrees.
a and b are the radius. Do you think that you could find the length of the line?

Answer 68

no.. ll

Answer 69

Ok, we have this here,

Ignore how badly drawn it is.
We have
a=24
b=24
C=120 deg
c=?
when we plug that into the formula we have
\[c^2 = 24^2+24^2 - 2(24)(24)(\cos(120))\]