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## #1 2019-04-08 12:08:07

dAnta
Member
Registered: 2019-04-01
Posts: 8

### Areas of Polygons

Hello, I need some help on these following questions.

2. If a heptagon has an area of 130 in2, what is the measure of one side?

4. A regular hexagon rests on one of the flat sides and has a total height of 14ft. What is the measure of one of the hexagon’s sides?

5. Problem solver (worth 6 points):  Find the surface area and volume of the pool shown below when the sides, the twelve "bumpers" making up the perimeter of the pool, are 5 ft each and the depth of the pool is 6 ft.

Last edited by dAnta (2019-04-10 04:06:14)

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## #2 2019-04-08 13:37:39

ganesh
Registered: 2005-06-28
Posts: 27,841

### Re: Areas of Polygons

Hi dAnta,

These links maybe of some help:

Polygons

Regular Polygons

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #3 2019-04-08 19:39:43

bob bundy
Registered: 2010-06-20
Posts: 8,504

### Re: Areas of Polygons

hi dAnta

Welcome to the forum.

Several previous posts have covered these questions.  Try using the search facility.

Bob

ps.  Without the diagram we wouldn't be able to help with Q5 anyway.

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #4 2019-04-09 04:01:14

dAnta
Member
Registered: 2019-04-01
Posts: 8

### Re: Areas of Polygons

I have looked but I can't seem to make sense of them. I have been on those three questions for a little over a month. At this point, I am completely and utterly stuck.
P.S. I don't know how to upload the picture. It's the same as the users before me posted.

Last edited by dAnta (2019-04-09 04:04:54)

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## #5 2019-04-10 19:42:06

bob bundy
Registered: 2010-06-20
Posts: 8,504

### Re: Areas of Polygons

hi dAnta

The earlier questions from this worksheet had a polygon and a length of side and asked for the area.  How did you do these?  There are two formulas you might have used.  I don't want to use the wrong one and confuse you further.  Or did you just carry out a series of steps?  Please describe how you did these questions; then I can work from your strengths to help you with the final ones.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #6 2019-04-11 00:40:01

bob bundy
Registered: 2010-06-20
Posts: 8,504

### Re: Areas of Polygons

Here's a repeat of the diagram I made before for Q4.

AE is 14, so AG is 7.

The angle AFG is 60 when the shape is a hexagon, so you can use trigonometry to find AF

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #7 2019-04-12 05:40:26

dAnta
Member
Registered: 2019-04-01
Posts: 8

### Re: Areas of Polygons

I did not use a formula. I divided them up into triangles and there was a group of steps. I can find the answer if I have to find the area but it is harder when I have to find a side.

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## #8 2019-04-12 15:44:34

Monox D. I-Fly
Member
From: Indonesia
Registered: 2015-12-02
Posts: 1,565

### Re: Areas of Polygons

dAnta wrote:

I did not use a formula. I divided them up into triangles and there was a group of steps. I can find the answer if I have to find the area but it is harder when I have to find a side.

Pythagorean Theorem?

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

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## #9 2019-04-12 20:45:58

bob bundy
Registered: 2010-06-20
Posts: 8,504

### Re: Areas of Polygons

hi dAnta

I divided them up into triangles and there was a group of steps.

That's what I need you to tell me in detail.  I know of two different groups of steps and I want to use the same ones you use.  I don't want to confuse you further.

step 1.   I mark the middle of the polygon and draw lines out to the vertices so that the n sided polygon is divided into n identical triangles.  Each triangle is isosceles.

step 2 …………………………..

Thanks,

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #10 2019-04-19 10:18:30

dAnta
Member
Registered: 2019-04-01
Posts: 8

### Re: Areas of Polygons

I have already solved question 2. I need help with the 4th and 5th questions now.
I got this for question 4.

4. A regular hexagon rests on one of the flat sides and has a total height of 14 ft. What is the measure of one of the hexagon’s sides?

I drew a hexagon into 6 triangles. I used the middle bottom triangles. The height is 14.

Height for the triangle: 14/2=7

360/6=60

2*S.A+60=180

2*S.A.=120

S.A.=60

S=12.12*2

S=24.24ft

Last edited by dAnta (2019-04-19 10:19:43)

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## #11 2019-04-19 20:39:52

bob bundy
Registered: 2010-06-20
Posts: 8,504

### Re: Areas of Polygons

Hi dAnta,

When you have calculated a length or angle, it's a good idea to ask yourself 'is this answer reasonable?'. 24 is far too large for that triangle.  The method is ok up to the point where you make adj the subject of the equation.  It should be adj = 7 / tan(60)

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #12 2019-04-21 12:54:34

dAnta
Member
Registered: 2019-04-01
Posts: 8

### Re: Areas of Polygons

4. A regular hexagon rests on one of the flat sides and has a total height of 14 ft. What is the measure of one of the hexagon’s sides?
I drew a hexagon into 6 triangles. I used the middle bottom triangles. The height is 14.
Height for the triangle: 14/2=7
360/6=60
2*S.A+60=180
2*S.A.=120
S.A.=60
S=4.04*2
S=8.08ft

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## #13 2019-04-22 00:58:08

bob bundy
Registered: 2010-06-20
Posts: 8,504

### Re: Areas of Polygons

hi dAnta

Yes, that's what I made it!

From what I can remember the pool looks like this:

Here's a view from above.  It is not accurately drawn.

To get the area of the pool surface you can work out the area of the octagon (no reason why you shouldn't put the two halves together) and the area of the rectangle; then add them together.

Start by calculating the angle ACH.  The sides (such as CG) are given so you can work out AH and AC using trig.  Then you can work out the area of triangle ACG and times by 8 for the whole octagon.  The rectangle length (CF) is two sections long and the width is twice AC.

The pool is a prism so it's volume will be area of the top times by the height of the sides.

It's not clear if 'surface area' means just the water surface or the area of the whole prism.  You'll already know the first.  I'd work out the second as well just to make sure.  You'll need to double the top area so as to include the bottom and add on the sides.  These are all rectangles and there are 12 of them.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #14 2019-04-22 10:28:38

dAnta
Member
Registered: 2019-04-01
Posts: 8

### Re: Areas of Polygons

Okay, so how would I be able to find AH and AC?

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## #15 2019-04-22 22:23:35

bob bundy
Registered: 2010-06-20
Posts: 8,504

### Re: Areas of Polygons

AHC is a right angled triangle, so use trig.

Have you calculated angle ACH or HAC yet?

B

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #16 2019-04-23 10:20:14

dAnta
Member
Registered: 2019-04-01
Posts: 8

### Re: Areas of Polygons

No, I am not sure I can find it.

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## #17 2019-04-24 00:35:27

bob bundy
Registered: 2010-06-20
Posts: 8,504

### Re: Areas of Polygons

It's a regular octagon so you can work out the central angles such as GAC. That triangle is isosceles so you can work out ACH or use the right angle.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #18 2019-04-27 10:41:42

dAnta
Member
Registered: 2019-04-01
Posts: 8

### Re: Areas of Polygons

Area of octagon

360/8=45

2*S.A.+45=180

2*S.A.=135

S.A.=67.5

tan(67.5)=opp/2.5

Opp=tan(67.5)*2.5

Opp=6.03

Area=6.03*5/2

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