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#1 2013-09-15 11:37:02

demha
Full Member

Offline

Polygons and Review

Just need some help understanding some of these math problems and checking the ones I already did (if right/wrong). Thank you for your time:

1. An equilateral triangle with a side of 1 inch - Answer: A
A 0.43 sq in
B 0.56 sq in
C 0.89 sq in
D 0.23 sq in
E 0.19 sq in
F 0.54 sq in


2. A square with a side of 2 feet - Answer: B
A 9 sq ft
B 4 sq ft
C 2 sq ft
D 7 sq ft
E 3 sq ft
F 8 sq ft


3. A regular pentagon with a side of 3 centimeters - Answer: F
A 23.01 sq cm
B 12.34 sq cm
C 39.17 sq cm
D 9.46 sq cm
E 34.21 sq cm
F 15.48 sq cm


4. A regular hexagon with a side of 10 cm - Answer: D
A 641.25 sq cm
B 194.45 sq cm
C 361.25 sq cm
D 259.81 sq cm
E 105.22 sq cm
F 453.01 sq cm


5. A regular heptagon with a side of 7 inches. ***need help understanding how to solve***
A 178.06 sq in
B 294.16 sq in
C 169.21 sq in
D 358.91 sq in
E 157.36 sq in
F 277.91 sq in


6. A trapezoid where the height is 18 cm, base 1 = 16 cm and b2 = 8 cm. - Answer: C
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 230 sq cm
E 280.9 sq cm
F 510 sq cm


7. A trapezoid where the height = 7 mm, base 1    = 26 mm and base 2 = 9 mm. - Answer: B
A 178.06 sq mm
B 122.5 sq mm
C 216 sq mm
D 230 sq mm
E 28.9 mm
F 510 mm


Fill in the missing information for the following trapezoids:

8.
height = 19.8 cm
b1 = ________
b2 = 14.4 cm
area = 401.94 cm2 - Answer: A
A 26.2 cm
B 12.5 cm
C 216 cm
D 23 cm
E 28.9 cm
F 51 cm


9.
height = 23 mm
b1 = 23 mm
b2 = ________
area = 529 mm2 - Answer: D
A 78.06 sq mm
B 22.5 sq mm
C 21.6 mm
D 23 mm
E 28.9 mm
F 30 mm^2


10.
height = ________
b1 = 20 cm
b2 = 21 cm
area = 205 cm2 - Answer: D
A 17.06 cm
B 12.5 sq cm
C 26 cm
D 10 cm
E 28.9 cm
F 50 cm^2


11.
height = 28.9 m
b1 = 26.9 m
b2 = ________
area = 806.31 m^2 - Answer: E

A 17.06 sq m
B 15 m
C 46 m
D 23 m
E 28.9 m
F 51 m


12. If the area of a parallelogram is 690.84 m^2 and the height is 20.2 m, what is the length of the base? - Answer: D
A 78.06 m
B 22.5 m
C 216 m
D 34.2 m
E 28.9 m
F 51 m


13. If the base of a rectangle is 28 cm and the area is 588 cm^2, what is the height of the rectangle? - Answer: E

A 17.06 cm
B 122.5 sq cm
C 216 sq cm
D 23 cm
E 21 cm
F 51 cm^2


14. If the height of a rectangle is 26.1 m and the base is 17.3 m, what is the area of the rectangle? - Answer: A
A 451.53 m^2
B 122.5 m^2
C 216 m^2
D 430 m^2
E 289 m^2
F 510 m^2


15. If the height of a parallelogram is 34 cm and the base is 15 cm, what is the area of the parallelogram? - Answer: F
A 178.06 cm^2
B 122.5 cm^2
C 216 cm^2
D 230 cm^2
E 289 cm^2
F 510 cm^2


16. What is the area of a parallelogram with height 26 cm, base 16 cm, and side length 28 cm?***need help understanding how to solve***
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 416 cm^2
E 28.9 cm
F 510 cm^2


17. What is the area of a regular octagon with a side of 6 cm? ***need help understanding how to solve***
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 23 cm^2
E 173.82 cm^2
F 510 cm^2


18. What is the area of this polygon?***need help understanding how to solve***
http://www.compuhigh.com/linkme/admin/testeditor/upload/pics/geometry/lesson21/area1.gif


ls_XF    =    53 mm    ls_XV    =    72 mm    ls_VR    =    16 mm
ls_FB    =    31 mm    ls_BT    =    31 mm    ls_EU    =    47 mm
ls_UL    =    31 mm    ls_TL    =    88 mm    ls_DE    =    16 mm
ls_RM    =    70 mm    ls_MC    =    21 mm    ls_DC    =    70 mm



A 8014 mm2
B7030 mm2
C6027 mm2
D5478 mm2
E 1782 mm2
F 1225 mm2


19. What is the area of this rectangle?***need help understanding how to solve***
http://www.compuhigh.com/linkme/admin/testeditor/upload/pics/geometry/lesson21/area2.jpg


A 17.06 sq units
B60 sq units
C21.6 sq units
D53 sq units
E 28.9 sq units
F 51 sq units


20. What is the area of this polygon?***need help understanding how to solve***
http://www.compuhigh.com/linkme/admin/testeditor/upload/pics/geometry/lesson21/area3.jpg


A 178 sq units
B129 sq units
C230 sq units
D240 sq units
E 219 sq units
F 206 sq units


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

#2 2013-09-15 17:37:30

bob bundy
Moderator

Online

Re: Polygons and Review

hi demha

I assume you are asked for the areas here. 

1. An equilateral triangle with a side of 1 inch - Answer: A
A 0.43 sq in
B 0.56 sq in
C 0.89 sq in
D 0.23 sq in
E 0.19 sq in
F 0.54 sq in

Correct. 

2. A square with a side of 2 feet - Answer: B
A 9 sq ft
B 4 sq ft
C 2 sq ft
D 7 sq ft
E 3 sq ft
F 8 sq ft

Correct. 

3. A regular pentagon with a side of 3 centimeters - Answer: F
A 23.01 sq cm
B 12.34 sq cm
C 39.17 sq cm
D 9.46 sq cm
E 34.21 sq cm
F 15.48 sq cm

Correct. 

4. A regular hexagon with a side of 10 cm - Answer: D
A 641.25 sq cm
B 194.45 sq cm
C 361.25 sq cm
D 259.81 sq cm
E 105.22 sq cm
F 453.01 sq cm

Correct. 

5. A regular heptagon with a side of 7 inches. ***need help understanding how to solve***
A 178.06 sq in
B 294.16 sq in
C 169.21 sq in
D 358.91 sq in
E 157.36 sq in
F 277.91 sq in

How did you do the previous ones?  I'm doing them like this:  (i) 360/7 to get the central angle for one of 7 identical triangles. (ii) Split this angle in half to create a right angled triangle (iii) Use tan to get the height of the triangle (iv) half base x height for the area of one (v) x by 7 to get area of heptagon 


6. A trapezoid where the height is 18 cm, base 1 = 16 cm and b2 = 8 cm. - Answer: C
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 230 sq cm
E 280.9 sq cm
F 510 sq cm

Correct. 

7. A trapezoid where the height = 7 mm, base 1    = 26 mm and base 2 = 9 mm. - Answer: B
A 178.06 sq mm
B 122.5 sq mm
C 216 sq mm
D 230 sq mm
E 28.9 mm
F 510 mm

Correct. 

Fill in the missing information for the following trapezoids:

8.
height = 19.8 cm
b1 = ________
b2 = 14.4 cm
area = 401.94 cm2 - Answer: A
A 26.2 cm
B 12.5 cm
C 216 cm
D 23 cm
E 28.9 cm
F 51 cm

Correct. 

9.
height = 23 mm
b1 = 23 mm
b2 = ________
area = 529 mm2 - Answer: D
A 78.06 sq mm
B 22.5 sq mm
C 21.6 mm
D 23 mm
E 28.9 mm
F 30 mm^2

Correct. 

10.
height = ________
b1 = 20 cm
b2 = 21 cm
area = 205 cm2 - Answer: D
A 17.06 cm
B 12.5 sq cm
C 26 cm
D 10 cm
E 28.9 cm
F 50 cm^2

Correct. 

11.
height = 28.9 m
b1 = 26.9 m
b2 = ________
area = 806.31 m^2 - Answer: E

A 17.06 sq m
B 15 m
C 46 m
D 23 m
E 28.9 m
F 51 m

Correct. 

12. If the area of a parallelogram is 690.84 m^2 and the height is 20.2 m, what is the length of the base? - Answer: D
A 78.06 m
B 22.5 m
C 216 m
D 34.2 m
E 28.9 m
F 51 m

Correct. 

13. If the base of a rectangle is 28 cm and the area is 588 cm^2, what is the height of the rectangle? - Answer: E

A 17.06 cm
B 122.5 sq cm
C 216 sq cm
D 23 cm
E 21 cm
F 51 cm^2

Correct. 

14. If the height of a rectangle is 26.1 m and the base is 17.3 m, what is the area of the rectangle? - Answer: A
A 451.53 m^2
B 122.5 m^2
C 216 m^2
D 430 m^2
E 289 m^2
F 510 m^2

Correct. 

15. If the height of a parallelogram is 34 cm and the base is 15 cm, what is the area of the parallelogram? - Answer: F
A 178.06 cm^2
B 122.5 cm^2
C 216 cm^2
D 230 cm^2
E 289 cm^2
F 510 cm^2

Correct. 

16. What is the area of a parallelogram with height 26 cm, base 16 cm, and side length 28 cm?***need help understanding how to solve***
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 416 cm^2
E 28.9 cm
F 510 cm^2

You only need two measuements.  They have given you an extra measurement just to make sure you know which two to multiply together. 

17. What is the area of a regular octagon with a side of 6 cm? ***need help understanding how to solve***
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 23 cm^2
E 173.82 cm^2
F 510 cm^2

Split this into 8 triangles.  The angle at the top of each triangle is 360/8 and then you need to half this to make a right angle for the tangent calculation. 

18. What is the area of this polygon?***need help understanding how to solve***

You can split this polygon onto three rectangles.  (see picture below)  You will have to use the information to work out the length and width of each part and then add up the areas.

ls_XF    =    53 mm    ls_XV    =    72 mm    ls_VR    =    16 mm
ls_FB    =    31 mm    ls_BT    =    31 mm    ls_EU    =    47 mm
ls_UL    =    31 mm    ls_TL    =    88 mm    ls_DE    =    16 mm
ls_RM    =    70 mm    ls_MC    =    21 mm    ls_DC    =    70 mm



A 8014 mm2
B7030 mm2
C6027 mm2
D5478 mm2
E 1782 mm2
F 1225 mm2


19. What is the area of this rectangle?***need help understanding how to solve***

Use Pythagoras to work out the height of the rectangle.

A 17.06 sq units
B60 sq units
C21.6 sq units
D53 sq units
E 28.9 sq units
F 51 sq units


20. What is the area of this polygon?***need help understanding how to solve***

My picture below shows how you can split this shape into a rectangle and a triangle.  You will also need to use Pythag. to get the length of the red line.

A 178 sq units
B129 sq units
C230 sq units
D240 sq units
E 219 sq units
F 206 sq units



Hope that helps  smile

Bob


Uploaded Images
View Image: demha5.gif      


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#3 2013-09-15 20:12:18

demha
Full Member

Offline

Re: Polygons and Review

Thank you for your reply Bob and yes, your assumption is correct, we are looking for the area here. I will begin with 5:
5. A regular heptagon with a side of 7 inches. ***need help understanding how to solve***
A 178.06 sq in
B 294.16 sq in
C 169.21 sq in
D 358.91 sq in
E 157.36 sq in
F 277.91 sq in
360/7 = 51.42 (central angle)
51.42/2 = 25.71 | 25.71tan = 0.48
51.42 x 0.48 = 24.6768 x 7 = 172.7712

I'm not understanding what went wrong here.

---
16. What is the area of a parallelogram with height 26 cm, base 16 cm, and side length 28 cm?
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 416 cm^2
E 28.9 cm
F 510 cm^2

Makes sense! Answer is D - 416 cm^2



17. What is the area of a regular octagon with a side of 6 cm? ***need help understanding how to solve***
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 23 cm^2
E 173.82 cm^2
F 510 cm^2

360/8 = 45
half it so 45/2 = 22.5
Am I right so far? If so, would the next step be 22.5tan?



18. What is the area of this polygon?***need help understanding how to solve***

You can split this polygon onto three rectangles.  (see picture below)  You will have to use the information to work out the length and width of each part and then add up the areas.

ls_XF    =    53 mm    ls_XV    =    72 mm    ls_VR    =    16 mm
ls_FB    =    31 mm    ls_BT    =    31 mm    ls_EU    =    47 mm
ls_UL    =    31 mm    ls_TL    =    88 mm    ls_DE    =    16 mm
ls_RM    =    70 mm    ls_MC    =    21 mm    ls_DC    =    70 mm



A 8014 mm2
B7030 mm2
C6027 mm2
D5478 mm2
E 1782 mm2
F 1225 mm2

Takes a little while but got the answer: A - 8014 mm2



19. What is the area of this rectangle?***need help understanding how to solve***

Use Pythagoras to work out the height of the rectangle.

A 17.06 sq units
B60 sq units
C21.6 sq units
D53 sq units
E 28.9 sq units
F 51 sq units

So this is the equation I started with: H^2 = 13^2 - 12^2
Am I starting right?



20. What is the area of this polygon?***need help understanding how to solve***

My picture below shows how you can split this shape into a rectangle and a triangle.  You will also need to use Pythag. to get the length of the red line.

A 178 sq units
B129 sq units
C230 sq units
D240 sq units
E 219 sq units
F 206 sq units

Not exactly sure where to start on this.


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

#4 2013-09-16 03:34:01

bob bundy
Moderator

Online

Re: Polygons and Review

hi demha

5. A regular heptagon with a side of 7 inches. ***need help understanding how to solve***
A 178.06 sq in
B 294.16 sq in
C 169.21 sq in
D 358.91 sq in
E 157.36 sq in
F 277.91 sq in
360/7 = 51.42 (central angle)
51.42/2 = 25.71 | 25.71tan = 0.48

  When a triangle is split in half to get a right angle, the opposite is 7/2 = 3.5 and the height is the adjacent.  So you want A = 3.5/tan(22.5)
51.42 x 0.48 = 24.6768 x 7 = 172.7712

I'm not understanding what went wrong here.

---
16. What is the area of a parallelogram with height 26 cm, base 16 cm, and side length 28 cm?
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 416 cm^2
E 28.9 cm
F 510 cm^2

Makes sense! Answer is D - 416 cm^2

  Correct. 

17. What is the area of a regular octagon with a side of 6 cm? ***need help understanding how to solve***
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 23 cm^2
E 173.82 cm^2
F 510 cm^2

360/8 = 45
half it so 45/2 = 22.5
Am I right so far? If so, would the next step be 22.5tan?


22.5 is correct.  But look at question 5.  Again the height is the adjacent. 



18. What is the area of this polygon?***need help understanding how to solve***

You can split this polygon onto three rectangles.  (see picture below)  You will have to use the information to work out the length and width of each part and then add up the areas.

ls_XF    =    53 mm    ls_XV    =    72 mm    ls_VR    =    16 mm
ls_FB    =    31 mm    ls_BT    =    31 mm    ls_EU    =    47 mm
ls_UL    =    31 mm    ls_TL    =    88 mm    ls_DE    =    16 mm
ls_RM    =    70 mm    ls_MC    =    21 mm    ls_DC    =    70 mm



A 8014 mm2
B7030 mm2
C6027 mm2
D5478 mm2
E 1782 mm2
F 1225 mm2

Takes a little while but got the answer: A - 8014 mm2

  Correct. 


19. What is the area of this rectangle?***need help understanding how to solve***

Use Pythagoras to work out the height of the rectangle.

A 17.06 sq units
B60 sq units
C21.6 sq units
D53 sq units
E 28.9 sq units
F 51 sq units

So this is the equation I started with: H^2 = 13^2 - 12^2
Am I starting right?

  Yes.  smile 


20. What is the area of this polygon?***need help understanding how to solve***

My picture below shows how you can split this shape into a rectangle and a triangle.  You will also need to use Pythag. to get the length of the red line.

A 178 sq units
B129 sq units
C230 sq units
D240 sq units
E 219 sq units
F 206 sq units

Not exactly sure where to start on this.

  see diagram below. 

Bob


Uploaded Images
View Image: demha6.gif      


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#5 2013-09-16 08:41:58

demha
Full Member

Offline

Re: Polygons and Review

5. A regular heptagon with a side of 7 inches.
A 178.06 sq in
B 294.16 sq in
C 169.21 sq in
D 358.91 sq in
E 157.36 sq in
F 277.91 sq in

I'm having a hard time understanding how to solve this and #17. Do you think you could create a similar math problem and then show me how to solve it step by step? For example maybe you can do the same as #5, except with a side of 5 instead of 7 inches.

---

17. What is the area of a regular octagon with a side of 6 cm?
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 23 cm^2
E 173.82 cm^2
F 510 cm^2

Same as #5.


---

19. What is the area of this rectangle?

Use Pythagoras to work out the height of the rectangle.

A 17.06 sq units
B 60 sq units
C 21.6 sq units
D 53 sq units
E 28.9 sq units
F 51 sq units z

H^2 = 13^2 - 12^2
H^2 = 169 - 144
H^2 = 25
H = 5

Not too sure what I did wrong here.



20. What is the area of this polygon?

My picture below shows how you can split this shape into a rectangle and a triangle.  You will also need to use Pythag. to get the length of the red line.

A 178 sq units
B 129 sq units
C 230 sq units
D 240 sq units
E 219 sq units
F 206 sq units

Ok so the rectangle area is 152 and the triangle area is 54. Add them together to get 206 which will be the answer: F - 206 sq units.


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

#6 2013-09-16 20:45:16

bob bundy
Moderator

Online

Re: Polygons and Review

hi demha

Q5 and Q17

Ok good idea.  Here's a nonagon example.  Diagram below.

Let's say  side AB = 6 cm.  M is midpoint AB so angle OMA = 90.

angle AOB = 360/9 = 40  => angle AOM = 20

OM is adjacent to this angle; AM is opposite => OM = 3/tan(20)

=> area AOB = 0.5 x 6 x 3/tan(20)

=> area of nonagon = 9 x 0.5 x 6 x 3/tan(20)



19. What is the area of this rectangle?

Use Pythagoras to work out the height of the rectangle.

A 17.06 sq units
B 60 sq units
C 21.6 sq units
D 53 sq units
E 28.9 sq units
F 51 sq units z

H^2 = 13^2 - 12^2
H^2 = 169 - 144
H^2 = 25
H = 5

Not too sure what I did wrong here.

No, nothing wrong, that's OK.  But now you want the area .....


20. What is the area of this polygon?

My picture below shows how you can split this shape into a rectangle and a triangle.  You will also need to use Pythag. to get the length of the red line.

A 178 sq units
B 129 sq units
C 230 sq units
D 240 sq units
E 219 sq units
F 206 sq units

Ok so the rectangle area is 152 and the triangle area is 54. Add them together to get 206 which will be the answer: F - 206 sq units.

Correct! 

Bob


--------------------------------------------------------------------------------
"The thing about quotes on the Internet is you cannot confirm their validity"


Uploaded Images
View Image: demha7.gif      


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#7 2013-09-17 00:17:54

demha
Full Member

Offline

Re: Polygons and Review

5. A regular heptagon with a side of 7 inches.
A 178.06 sq in
B 294.16 sq in
C 169.21 sq in
D 358.91 sq in
E 157.36 sq in
F 277.91 sq in

360/7 = 51.42 => 25.71

3/tan(25.71)

7 x 0.5 x 7 x 3/tan(25.71)

Am I going the correct way with this? If so, how would I solve here? This is as far as I went:
24.5 x 3/tan(25.71)

---
19. What is the area of this rectangle?

Use Pythagoras to work out the height of the rectangle.

A 17.06 sq units
B 60 sq units
C 21.6 sq units
D 53 sq units
E 28.9 sq units
F 51 sq units z

H^2 = 13^2 - 12^2
H^2 = 169 - 144
H^2 = 25
H = 5

So now I know that Height = 5 and Base = 12, SO 5 x 12 = 60 sq units which is answer B.


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

#8 2013-09-17 03:15:56

bob bundy
Moderator

Online

Re: Polygons and Review

Q19 is now correct.  Well done.

Q5 has a minor error.

5. A regular heptagon with a side of 7 inches.
A 178.06 sq in
B 294.16 sq in
C 169.21 sq in
D 358.91 sq in
E 157.36 sq in
F 277.91 sq in

360/7 = 51.42 => 25.71

3/tan(25.71)

AM is half AB

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#9 2013-09-17 03:39:30

demha
Full Member

Offline

Re: Polygons and Review

Oh so it's 7/2 = 3.5, then

7 x 0.5 x 7 x 3.5/tan(25.71)

If this is correct, how would I solve it from here?


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

#10 2013-09-17 04:10:59

bob bundy
Moderator

Online

Re: Polygons and Review

Yes, that's it.  Just grab your calculator and work it out.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#11 2013-09-17 07:17:52

demha
Full Member

Offline

Re: Polygons and Review

5. A regular heptagon with a side of 7 inches.
A 178.06 sq in
B 294.16 sq in
C 169.21 sq in
D 358.91 sq in
E 157.36 sq in
F 277.91 sq in

Took me a second to figure out how to do it but i got the answer of A - 178.06 sq. in.


---

17. What is the area of a regular octagon with a side of 6 cm?
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 23 cm^2
E 173.82 cm^2
F 510 cm^2

360/8 = 45/2 = 22.5

8 x 0.5 x 6 x 3/tan(22.5) = 173.82 cm^2
So the answer is E

THANK YOU!!!


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

#12 2013-09-17 07:22:29

demha
Full Member

Offline

Re: Polygons and Review

Sent them in, 20/20. I thank you VERY much Mr. Bob for your help!


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

#13 2013-09-17 07:57:08

bob bundy
Moderator

Online

Re: Polygons and Review

Well that is splendid!  I am really pleased too.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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