Math Is Fun Forum

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)

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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.

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.

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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.

Finished with this lesson! Thank you very much Bobbym for your help. Much appreciated!!

Ok here is the "redo" for #7 - #10:
7. When the rope goes around the barn, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?
Answer:  The new radius is 30. It can make up to ¼. So the area would be:
1/4 x 30^2 x PI
1/4 x 900 x PI
225 (PI) = 706.858

8. When the rope goes around the barn the other way, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?
Answer: The radius is 30. It can make up to ¼. So the area would be:
1/4 x 30^2 x PI
1/4 x 900 x PI
225 (PI) = 706.858

9. The areas you found in 7 and 8 overlap each other. How much do they overlap? What *approximate* shape do they make? What is that area?
Answer:  I would say that the area is 75. It looks like it almost makes a square shape.

10. What is the total grazing area the goat can reach?
Answer: To get this answer, I added up the ansers of #6, #7 and #8 then subtracted the answer from #9:
1875(PI) + 225(PI) + 225(PI) – 75
2325(PI) – 75
7304.202 – 75
7229.202 is the final answer.

Cool! So it would be:
3/4 x 10^2 x PI
3/4 x 100 x PI
75 (PI) is the final answer or 235.619

And #7 and #8 are literally asking for the same thing. So the equation for them both would be:
1/4 x 30^2 x PI
1/4 x 900 x PI
225 (PI) is the final answer or 706.858 - is this correct?

Yes I understand that. The E-circle represents the entire range, the F-circle and G-circle represent the both ways the goat can go, and the H-circle (green) represents where they overlap. So would this just be considered as one area, as in just 10? Making the equation:
1/4 x 10^2 x PI

Am I following the right path here?

Yes I keep getting mixed up so sorry! The rope goes around the barn 3/4. But I have been thinking that #7 and #8 will be the same equation:
3/4 x 30^2 x PI

I know there is 10 left but that is what we can use for #9? It asks "The areas you found in 7 and 8 overlap each other. How much do they overlap? What *approximate* shape do they make? What is that area?" So I came to believe that the equation for THIS number will be:
1/4 x 10^2 x PI

Am I right on this?

Can we use the image for #6 to #10?

Yes, and then there will be 10 feet left just enough to get around another corner.

So I add them together to get 40 THEN do the equation?

That's great to hear! What about 7 & 8?

Somewhat, I kind of drew one on paper and based it on that. #9 and #10 i am finding a little difficult to find the answer.