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Hello,
Thank you for your cooperation. If you could delete this post as well that would be awesome!
Thank you for all the help,
Kayla
Hello,
I'd appreciate it if you could delete this post as well!
Thank you again,
Kayla
Hello,
Thanks for all the help, but if you could take down this post as well as the others I'd appreciate it!
Thanks,
Kayla
Hello,
Could you delete this post as well?
Thank you!
Kayla
Hello,
Again I would greatly appreciate if you could take down this post as well. My school and I were very pleased that you took down the other post, so thank you!
Kayla
Hello,
#4: So, is the correct answer D, because each diagonal gets counted twice instead of once. Is that why there are 4 diagonals and not 2?
#12: Yes, the angles do add up to 180 degrees and that is why I originally put C. Do you also think the correct answer is D?
#14: Okay, I will try E and I will let you know if that is correct.
#17: So, the new answer is F?
Sorry for the confusion,
Kayla
Hello,
I have some questions about proofs.
#4: A square has two diagonals.
AGiven
B unfounded
C definition of an octagon
DThe number of diagonals is (n-3)n/2, where n is the number of sides, which is 4 for a square.
E 1267200 inches
F Definition of supplementary angles
I put B originally and it was wrong. I believe the correct answer is A.
12. In a triangle, if I have two angles that add up to 50 degrees, the remaining angle must be 130 degrees.
AGiven
B unfounded
C Definition of supplementary angles
DSum of angles in a triangle
E Definition of triangle inequality
F Definition of radius
I put C originally and it was wrong. I believe the correct answer is D.
14. If a central angle is 30 degrees, then the arc it defines is also 30 degrees.
AGiven
BDefinition of an inscribed angle
C unfounded
D Properties of a central angle
E Properties of an arc
F Definition of radius
I originally put C and it was wrong. I believe the correct answer is E.
17. If a circle has a central point M, and both point A and point D are on the circle, then ls_MA and ls_MD will be equal.
AGiven
B unfounded
C Definition of a line segment
D Definition of supplementary angles
E Definition of a bisector
F Definition of radius
I originally put A, but it was wrong. I believe the correct answer is F or B.
Thank you for all the help,
Kayla
Hello,
I turned this into my teacher. I will let you know what she says!
Thank you,
Kayla
Hello,
No worries about not catching the mistake! Here is what I have...
360 / 7 = 51.428
51.428 / 2 = 25.714
90- 25.714 = 64.286
130 / 7 = 18.571
18.571 = 0.5 x s x s/2 x TAN(OAH)
18.571 = 0.5 x s x s/2 x TAN(64.286)
18.571 = 0.5 x s x s/2 (2.076)
4(18.571) = s^2 (2.076)
4(18.571) / 2.076
= 74.284 / 2.076
= 35.782
Then I took the square root of 35.782 and I got 5.981
s = 5.981
Is this correct?
Thanks again for all the help!
Kayla
Hello,
This is what I got when I multiplied by 4.
4(18.571) = s^2 (0.481)
4(18.571) / 0.481
= 74.284 / 0.481
= 154.436
The square root of 154.436 = 12.427
s= 12.427 in
Is this the final answer? Also, why do you multiply by 4?
Thank you,
Kayla
Hello,
Okay, this is what I got from the information you gave me.
130 / 7 = 18.571. (This is the area of one triangle)
51.428 / 2 = 25.714 = angle OAH
18.571 = 0.5 x s x s/2 x TAN (OAH)
18.571 = 0.5 x s x s/2 x TAN (25.714)
18.571 = 0.5 x s x s/s (0.481)
s^2= 18.571 x 0.5 x 0.481
s^2= 4.466 (I the took the square root)
s= 2.113
I'm not sure if this is correct. Thank you again for the help,
Kayla
Hello,
Do you know if this is correct?
Thank you,
Kayla
Hello,
Do you know what the next step is?
Thank you for all the help,
Kayla
Hello,
360 / 7 = 51.428 = angle EOD
51.428 / 2 = 25.714
25.714 = AOH
Now I am unsure of how you get AB with only knowing the area. AB is our base in the triangle AOB and the base and height are unknown and we only know the area. How can we find the side AB if we only know the area? After this step, I believe I know how to solve the rest, but I am unsure of how to solve for AB.
Thank you again,
Kayla
Hello,
When I solved 7 / cos(30) I got 8.083. Is this correct? Is this the length of one of the hexagon's side?
Thank you so much for the help. You have really helped me understand the material.
Kayla
Hello,
This is similar to a question I have asked before. My teacher says the formula I used was incorrect, so I was wondering if you could help me out. This is the question and what I have so far.
2. If a heptagon has an area of 130 in2, what is the measure of one side?
360 / 7 = 51.428
180 - 51.2 / 2 = 64.25
Tan (64.25) = opp. / adj.
Tan (64.25) = h (s/2)
My teacher wants me to solve this for h but leave s as a variable in your equation.
A = 1/2 bh (What is the area of one triangle? What is the expression for h in terms of s? What is the expression for b in terms of s?)
I am unsure of how you complete this, so if you could help that would be awesome.
Thank you again! You and your team have been very helpful!
Kayla
Hello,
AF= 14/cos (30)
I did several different ways because I was unsure which one was correct.
14/cos = 0.970 (30) = 420
30/cos = 0.866 (14) = 420
cos 30 = 0.866 (14) = 12.124
Thank you again for the help,
Kayla
Hello,
Would it be AF = 14/cos (60) and then solve?
I'm sorry this lesson was very hard for me to understand and master the concept. That's why I have lots of questions and confusion about it.
Thank you so much for all the help,
Kayla
Hello,
This is #4:
360 / 6 = 60
180 - 60 / 2 = 60
Cos (60) = opp. / adj.
Cos (60) = h (s/2)
7 = Cos 60 * (s/2)
s/2 = Cos 60 * 7
s/2 = .5 * 7
s/2 = 3.5
s = 1.75
(½) * base * height
(½) * 1.75 * 7
= 6.125 (7)
= 42.875 ft^2
42.875 / 7 / 1.75 / ½
= 7
The length of one side is 7 ft.
Hello,
Thank you for responding. My teacher wanted me to use trigonometry and the area of polygons to get these answers. This is what I have so far.
#2:
520/7 = s^2 * cot (180/ 7)
s^2 = 35. 774
s = 5.9811
The measure of one side of the heptagon with an area of 130 in^2 is 5.9811 in.
#3:
360 / 8 = 45
45 degrees / 2 = 22.5 degrees
This creates two 90°-22.5°-67.5° triangles.
R*Cos(22.5) = 0.92338*R = 0.92388*6 cm = 5.543 cm.
The shorter leg can be found by R*Sin(22.5) = 0.38268*R = 0.38268*6 cm = 2.296 cm.
1/2*b*h = 1/2*(5.543 cm)*(2.296 cm) = 6.364 cm^2
8 * 12.728 = 101.82 cm^2
The whole area of the octagon is 101.82 cm^2.
#4:
Tan (60) = opp. / adj.
Tan (60) = h (s/2)
7 = tan 60 * (s/2)
s/2 = tan 60 * 7
s/2 = 12.124
s = 6.062
(½) * base * height
(½) * 6.062 * 7
= 21.217 (7)
= 148.159 ft^2
= 148 ft ^2
148 / 7 / 6.062 / ½
= 6.975
The length of one side is 6.975 ft.
#5: My teacher said, "The two shapes must be REGULAR polygons. Two 6-sided figures will not have equal sides and equal angles." This is what I got for her to respond with that. I am confused on how to fix it.
I split the pool into 2 polygons with 6 sides each.
360 / 6 = 60
180 - 60 / 2 = 60
Tan (60) = opp. / adj.
Tan (60) = h (s/2)
h= tan 60 * 2.5 (half of the side)
1.732 * 2.5
= 4.330
(½) * base * height
(½) * 5 * 4.330
= 10.825 (6)
=64.95 (the area of one polygon)
64.95 (2)
= 129.9
130 ft^2 is the surface area of the pool.
129.9 (6)
= 779.4
180 ft^2 is the volume of the pool.
Hello,
I need some help on these math problems. I have been stuck on them for awhile.
Thank you,
Kayla
2. If a heptagon has an area of 130 in2, what is the measure of one side?
3. An octagon’s radius (measure from center to vertex) measures 6 cm, what is the octagon’s area?
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?
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.
Use your logic and the formulas you have learned so far for the area of polygons, surface area, and volume to calculate the surface area of the inside of the pool in the picture (the pool liner) and the volume of the pool if it was filled all the way to the top. Use the shape of the pool and include formulas that you have learned in class. (You cannot add or take out water to find the volume.)
- This 12 sided pool is not a regular polygon because the inner angles are not all equal. You will need to break the base of the pool down into 2 regular polygons.
- Show your work step-by-step just as you have done for #1-4 above. You may need to include some written explanations for what you are doing in each step. Show all of the work to find all of the areas necessary for the surface area and all of the work to find the volume.
Hello,
I am having some troubles in a lesson called Area of Polygons.
We are supposed to figure out the area of a polygon by cutting the polygon into triangles and finding the area from there. I am a little confused on how to do this. I know how to get the area of each of the questions with just the formula but I don't know how to do it with polygons. Below I posted the lesson. For questions 14 and 15 I can attach a link so you can view the pictures. I will do that when we get to those questions. just let me know.
Thank you so much,
Kayla
For 1-7, calculate the area for each of the polygons described below. If the shape is a regular polygon with more than 4 sides, divide the polygon into triangles as shown in the lesson. Show your work using only formulas for 3- and 4-sided figures as your basis. (Round answers to the nearest hundredth and remember to include the unit of measure.)
1. An equilateral triangle with a side of 1 inch
2. A square with a side of 2 feet
3. A regular pentagon with a side of 3 centimeters
4. A regular hexagon with a side of 10 cm
5. A regular heptagon with a side of 7 inches.
6. A trapezoid where the height is 18 cm, base 1 = 16 cm and b2 = 8 cm.
7. A trapezoid where the height = 7 mm, base 1 = 26 mm and base 2 = 9 mm.
For 8 and 9, fill in the missing information for the following trapezoids. SHOW YOUR WORK.
8.
height = 19.8 cm
b1 = ________
b2 = 14.4 cm
area = 401.94 cm2
9.
height = ________
b1 = 20 cm
b2 = 21 cm
area = 205 cm2
10. If the area of a parallelogram is 690.84 m2 and the height is 20.2 m, what is the length of the base?
11. If the base of a rectangle is 28 cm and the area is 588 cm^2, what is the height of the rectangle?
12. What is the area of a parallelogram with height 26 cm, base 16 cm, and side length 28 cm?
13. What is the area of this polygon?
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
14. What is the area of this rectangle?
15. What is the area of this polygon?
Hi bob bundy,
Okay so I took PIr^2 = 157.079 and I solved. I took the formula A/PI = r^2. I then plugged in my numbers. I got 157.079/ PI = 49.999. I then took that and got the square too to find r. (49.999 = r^2). After getting the square root the answer is 7.071. So, the radius of a half-piece is 7.071.
Is this correct?
Thank you again,
Kayla
Hi bob bundy,
I have gotten the area of the circle which is 314.159. I calculated half of that and got 157.079. (I took 314.159 and divided by 2). I am confused on what the next step is and how you work "backward".
Thanks,
Kayla
Hello,
Here is a link to the image with the question and some pictures. I am working on #5. I have gotten all the other answers correct. In the last post, I posted what I believe the answer is. If you could let me know if that is correct, that would be awesome!
Here's the link: https://imgur.com/tdFRvsY
Thanks,
Kayla