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Daniel Selman and Maegan Gugliotta

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Sally is planning a picnic for her friends and all of their dolls. She wants this to be the best picnic out of all of the picnics planned by any of her friends. All of her friends were making their own picnic blankets. One was making a 14-gon, so she decided to make hers better!!

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Since she wanted her picnic blanket to be better she wanted to make it a 15-gon. She didn’t have any measuring tools, so she measured out the ground with her hands. She estimated that she would need about 600 hands worth of material.

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She went to the local fabric store and purchased 1,800 hands worth of material. After that she went to the local convenience store to pick up all the treats for her friends.

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Once she got home she started working out the problems to find out the area and length of each side. She decided that she wanted each side to be 10 hands. So using that information, she divided the 15-gon into 15 different equilateral triangles.

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After Sally divided the 15-gon into different triangles, she determined that the central angle of all of these triangles would add up to be 360 degrees. She divided 360 degrees by 15, and each angle came out to be 24 degrees.

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Sally divided a triangle down the middle to get two right triangles, and since she knows one angle is perpendicular, it is 90 degrees. The central angle is divided by two so it is now 12 degrees. After adding the two angles together (90+12=102), she subtracted 102 from 180 and determined that the last angle was 78 degrees.

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In order to find the height of the triangle Sally typed in her calculator: 5tan(78). It came out to be 23.5 hands. Sally used the formula A=1/2b(h) to find the area of each equilateral triangle. A=1/2(10)(23.5)=117.5 hands

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Since Sally divided the 15-gon into 15 triangles and she knows the area of each of those triangles is 117.5 hands, she can now find the entire area of the picnic blanket. A=15(117.5)=1762.5 hands.

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Sally was able to create her 15-gon picnic blanket. She had the best picnic out of all of her friends. They all loved it so much that she had already began to plan her next picnic.

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THE END!

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