
The boy is trying to make parachutes for his science project. One is a pyramid, one is round, and one is an octagon. To be similar, he wants to make them have a similar surface area. We want to figure out the octagon area. Do we have enough factors? So we broke it down into the surface area of the 8 triangles in the octagon. As though it was a flat sheet of paper. If the original diameter of the circle (before cutting the edge off) is 50 cm, then each of the two sides is 25 cm (a radius, right?). The angles will always be 67.5, 67.5 and 45 (right?). So what is the formula? What size is the base of these triangles? What size is the height of these triangles? Is the area of each of the triangles then multiplied by 8 to get the surface area? 
FollowUp Postings:

 Posted by west_gardener (My Page) on Wed, Dec 4, 13 at 18:06
Where is endorphinjunkie? I bet he would know the answer. 

 Posted by endorphinjunkie z7bAlabama (My Page) on Wed, Dec 4, 13 at 21:22
Side angle side formula. area = (1/2)(R^2)sin(45). There are 8 similar triangle in our octagon. so the total area is 1768 cm^2. This is close to the area of the circle before cutting. The area of the circle is 1963 cm^2. The height of the triangle is found using the equation h = R*sin(45). So height = 17.7 cm. If you want the length of each side of the octagon you could use the law of cosines. It turns out that each side will measure 19.3 cm. 

 Posted by anneliese_32 6 (My Page) on Thu, Dec 5, 13 at 7:17
So it takes a math question to bring our recluse around. If I had known that I would have asked some, except I could not even ask a logical one! I am so glad to know that you are here and wish you would be more but respect your reasons. Take care good friend and all the best. 

Giggling with glee! I did it! I brough him out. Endoroph! Yay! And now I can say, I miss your input, and hope all is well with you. Take care of you. Ok now. Thank you. The boy has not made it out of Algebra, even if if it is Honors, it still isn't Geometry, Trig, etc. and he's just not getting it. Which is frustrating him. But I hope, just giving him the numbers will be enough. I still won't be able to explain it in his spatial mind well enough, this is something daddy would be better at. He speaks the boy's language better than I when it comes to physics and math. Thank you! 

Dorph, glad to see you! I read Robin's post, but didn't really have the faintest idea of what she was asking. Thanks for explaining even if I still don't understand! :) 

One more question? What length is the base of the triangle? 

So is it 52.2cm? Using Pythag theorum. Right? 
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