Circumference and Area

siyanor · 2012-05-09 07:04:59

Hello there ,

we have the below picture which contain two parts,part A(the 8 sided polygon) and Part B (four semicircles).first we have to calculate the whole field Area and Circumference in X expression second we have to find out for what values of x, areas and the circumferences of A and B equal (not counting the diameters in B)?

My answer is :
Area (A)=2400-2x² Area(B)=Pi(x)²
Area(field)=Area (A)+Area(B)=2400-2x² +Pi(x)²

Circum(A) =200+(4√2 - 8)x Circum(B)=2√2(Pi+2)x
Circum(field)=Circum(A)+circum(B)=(200+(4√2 - 8)x)+(2√2(Pi+2)x)

second part of the question , i was thinking to equal the Area of each part with its circumference (but i didnt understand who im suppose to do that in semicircular without counting the diameters?

Would you please do me a favor and see if my calculation is correct?

Thank you

Last edited by siyanor (2012-05-09 07:05:44)

bobbym · 2012-05-09 07:25:17

Hi siyanor;

Welcome to the forum. Is there something missing from that drawing?

anonimnystefy · 2012-05-09 07:38:24

Hi

I think the whole area and circumference are good. I didn't understand the second part,though. What is supposed to be equal?

bobbym · 2012-05-09 07:43:22

Where does the 2400 come from? Oh sorry the 40 did not fit on my screen.

siyanor · 2012-05-09 07:46:31

Hello there,
No thats the complete draw .
Regarding the second part of question (we are on the same side).well the question is saying for what value of x perimeter and Area of each filed will be equal (meaning we have to put Area=Perimeter)
i didnt get the part that is saying without counting the diameter!

anonimnystefy · 2012-05-09 07:47:09

It's okay. I would just like some clarification from the OP.

siyanor · 2012-05-09 08:25:48

what do you mean by OP ?original Post ?

anonimnystefy · 2012-05-09 08:31:14

Hi siyanor

OP=Original Poster

Without diameters means that we don't count the part that connects the ends.of the two segments length x that have one common vertex.

|'''''''''''''''''/
|               /
|             /
|           /    <-------We don't include this side in our calculation of the circumference.
|         /
|       /
|     /
|   /
| /

Last edited by anonimnystefy (2012-05-09 08:31:36)

siyanor · 2012-05-09 08:44:07

But how am i suppose to do that ?considering we need diameter to calculate the area and perimeter of the circle ?
Im really confused ?

anonimnystefy · 2012-05-09 08:46:01

Hi siyanor

It doesn't say-you cannot use the length of the diameter. It says-don't include its length in the length of the circumference.

siyanor · 2012-05-09 08:54:39

so i have to substract it's length from the circumference ,right?

anonimnystefy · 2012-05-09 08:57:47

No. Just do not add it.

What they said is somewhat intuitive,and it seems they only caused confusion by adding that in.

siyanor · 2012-05-09 09:19:21

we say that circumference of a circle is (Pi*Diameter) or (Pi *r²), here because we have semicircular we have to multiply it by 1/2 ,what you mean by do not add Diameter ( im really not getting this )

anonimnystefy · 2012-05-09 09:20:39

It means that you just add the semi circles and those segments of rectangle sides between the.

siyanor · 2012-05-09 09:30:39

Thank you for replying .

I think i finally got what you are trying to say
but one more thing , lets say we want to find the length of around of the field(here we have to calculate the arc size ) how we are suppose to do that ?we can not use the Perimeter of the field ,thats for sure .

anonimnystefy · 2012-05-09 10:07:15

Hi

I don't understand your question. Could you clarify it a little bit?

siyanor · 2012-05-09 16:43:11

Hi,

we want to plant trees around the field for x= 5 and the minimum distance between each tree should be 2 meters ,the question is asking for quantity of trees that could be planted around the field.
we have to find the length of sides and arcs (we will not use diameters in this situation ).

Bob · 2012-05-09 20:20:14

hi siyanor

I've only just seen this and I'd like to backtrack a bit.

(1) "without counting the diameter". I've put a diagram below to show what I think it means. They want the perimeter shown in red.

(2) The area.

OK

(3) The perimeter.

Circum(A) =200+(4√2 - 8)x Circum(B)=2√2(Pi+2)x
Circum(field)=Circum(A)+circum(B)=(200+(4√2 - 8)x)+(2√2(Pi+2)x)

I'd do (perimeter of rectangle) - (8 straight line segments) + (4 semicircular arcs)

= (perimeter of rectangle) - (8 straight line segments) + (4 x circumference divide by 2)

= 200 - (8 . x) + 4 . ( 2 . pi . (√2 x/2) ÷ 2)

= 200 - 8x + 2√2 . pi . x

(4) Are these trees just around the perimeter or are we filling the whole field?

Bob

siyanor · 2012-05-09 21:36:32

Hi Bob Bundy,
Thank you for replying.
regarding the "without counting the diameter" part is asking us to find the value of x when areas and circumferences of A and B are equal. ( like we have to to write Area A=Area B , and then we can find the value of x.)

Regarding the trees, it will be only around the field ( exactly the area you have shown in red)

regarding your solution for perimeter :
= (perimeter of rectangle) - (8 straight line segments) + (4 x circumference divide by 2)
dont you think we are counting the diameter area in two places?!. i mean its been included in semicircle perimeter and in polygon perimeter (please correct me if I'm wrong).

Bob · 2012-05-09 22:19:27

hi siyanor,

dont you think we are counting the diameter area in two places?!.

I'm not trying to calculate an area here.

The perimeter is a length.

I've split my picture into bits to show what I'm calculating.

Based on your area formula (which I agree with) and my perimeter, I've tried to make them equal.

I get a quadratic with no real roots. (?)

Bob

siyanor · 2012-05-09 22:46:22

Hi Bob
I think you are absolutely right. thank you for making it so easy to understand
i guess the second part of the question that says "without counting the diameter ", is trying to say the same thing that you just said.
Thank you again

Bob · 2012-05-10 06:31:56

Finally I'm thinking properly (I hope)

The equal area and perimeter will never happen!

ignore for a moment the semicircles.

area of rectangle = 60 x 40 = 2400

perimeter of rectangle = (60 + 40) x 2 = 200

So the values are way, way apart!

Now chop off the triangles and add bigger semicircles. The area goes up. (maybe the perimeter does too but not by thousands)

So .....

(i) Is this diagram correct?

(ii) Is the wording correct?

(iii) Is the question setter having a laugh?

Bob

siyanor · 2012-05-10 10:42:58

bob bundy wrote:

hi siyanor,
dont you think we are counting the diameter area in two places?!.
Based on your area formula (which I agree with) and my perimeter, I've tried to make them equal.
I get a quadratic with no real roots. (?)
Bob

Hi Bob,
sorry i didnt see this part of your reply.i have resolved the quadratic equation for Area and the answer was x=-21.608 and x=21.608,and for sure we will be using the positive one.

siyanor · 2012-05-10 10:48:00

bob bundy wrote:

Finally I'm thinking properly (I hope)
The equal area and perimeter will never happen!
ignore for a moment the semicircles.
area of rectangle = 60 x 40 = 2400
perimeter of rectangle = (60 + 40) x 2 = 200
So the values are way, way apart!
Now chop off the triangles and add bigger semicircles. The area goes up. (maybe the perimeter does too but not by thousands)
So .....
(i) Is this diagram correct?
(ii) Is the wording correct?
(iii) Is the question setter having a laugh?
Bob

What the question is asking for what value of x so the Area and circumference of field A(polygon) will be equal to field B(it will be like Area(A)=Area(b) , and Circum(A)=Circum(B))

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#1 2012-05-09 07:04:59

Circumference and Area

#2 2012-05-09 07:25:17

Re: Circumference and Area

#3 2012-05-09 07:38:24

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#4 2012-05-09 07:43:22

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#5 2012-05-09 07:46:31

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#11 2012-05-09 08:54:39

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#12 2012-05-09 08:57:47

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#13 2012-05-09 09:19:21

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#15 2012-05-09 09:30:39

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#16 2012-05-09 10:07:15

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#17 2012-05-09 16:43:11

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#18 2012-05-09 20:20:14

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#19 2012-05-09 21:36:32

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#22 2012-05-10 06:31:56

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