The title of this POW is Going Global. In this problem you have to figure out the area of the field of Shakespeare’s Globe Theater. Using this you have to figure out how many people can stand in the field if they each need 4 square feet. The theater is an icosagon, this is a 20 sided figure. You have to figure out the interior angle. To figure out these problems you have to assume that the inner field is a circle and it is 12.5 feet away from the outside. The diameter of the icosagon is 100 feet. And the dimensions of the rectangular stage are 53 feet by 26.5 feet. The center of the front of the stage is the exact center of the building. The key math content in this POW is geometry because the whole POW is about finding areas and angles of shapes.
I solved the problem of how big the interior angle is by first cutting the icosagon into 20 triangles. Each triangle cut each interior angle in half. Then I noticed that there was a strait line going across the icosagon cutting it into two sets of ten triangles. A strait line is 180º, so I divided 180 by 10 = 18. I know that the total angle of a triangle is 180, so I subtracted 18 from 180 = 162. The two remaining angles were the same so I divided 162 by 2. But that is only half of the total interior angle so I multiplied it by 2. This told me the interior angle was 162º. I knew what to do because we spent a lot of time on angles in 6th and 7th grade and you explained a way to solve the problem.
I figured out how many people could stand in the field, by first figuring out how big the circle of the field would be if part of it was not cover by the stage or backstage. First I figured out how big the radius was. The diameter of the icosagon is 100 feet and the inner field is a circle and it is 12.5 feet away from the outside. I multiplied 12.5 by 2 = 25 I did this because there were 12.5 feet on each side. then I subtracted 25 from 100 = 75 to get the diameter. I divided 75 by 2 = 37.5 to get the radius. Then I squared the radius and multiplied it by pi to get the area of the circle (37.5 x 37.5 = 1,406.25 x 3.14 = 4,415.625 square feet). Then I found the area of the stage and subtracted it from the field circle (53 x 26.5 = 1,404.5)(4,415.625 - 1,404.5 = 3,011,125). I could not figure out how to find the part of the stage that was cut off by the backstage. When I went to school Owen helped me figure out that if you continued the draw of the field into the backstage and you drew lines from the edges of the backstage to the front center stage, you would cut the stage in half and the over all circle of the stage into a forth. I then divided the over all circle of the stage in froths(4,415.625/4 =1,103.90625), I divided the stage area in half (1,404.5/2 = 702.25), and then I subtracted the half of the stage by forth of the circle to get the part of backstage that was not part of the field (1,103.9625 - 702.25 = 401.7125). Then I subtracted the area of the field backstage from the area of the field minus the stage plus the area of the field backstage to get the area of the field (3,011.125 - 401.7125 = 2,609.4125). Then I divided the area of the field by 4 to get the total number of people that fit in the field (2,609.4125/4 =about 652 people). About 652 people fit in the field. My resources were my old math notebooks and my classmates.
My answer is the interior angle is 162º and 625 people can fit in the field. My answer is correct because I checked it with my classmates. I did not find a second answer. This POW reminded me of some of the Verdana POW’s were we had to use triangles to figure out areas of a circle and how long different routes from the adult village were.
What interested me about this problem was how logical it was to figure out how big the portion of the field was backstage once you thought about i for a while. And it surprised me how useful triangles were in a POW about circles and icosagons. What challenged me was figuring out how big the portion of field was backstage. I think I managed my time very well because I solved the POW in three days and wrote it up on the forth. But next time I should grapple with my problems a little longer before I ask for help.