St. Louis Science Center Planetarium Mathematics I.

Regular 72-gon Geometry

Solve the problem stated below and attach any graph paper graphs or diagrams. Turn this in to your teacher for class interest. If you wish to email your work to the address below - please use your initials in place of your name. You will probably not get a return response other than a smile. For helpful suggestions link here. For resource equations or formulas related to the St. Louis Science Center Planetarium click here: .

Problem(s): ( Print this page to work and turn in. )

The outside window's base line of level B form a regular polygon of 72 sides. We consider this wall of windows, lateral surface, a cylinder in other problems and after working this page you may wish to compare results. The perimeter of a regular 72-gon is 72 times the length of one side. The length of a side can be found by taking 2 times 70.51736 feet times the sine of 2.5 degrees.

a)     Why 2.5 degrees?

b)     Why sine of 2.5 degrees? Draw a picture of this and two other isosceles triangles in the arc of a circle of radius 70.51736 feet to scale to show the relationships in a part of this regular 72-gon.

c)     What is the length of a side of this regular 72-gon?

d)     What is the perimeter of this regular 72-gon?

e)     What is the lateral surface area of this regular 72-gon if the window height is 15.5 feet?

Write "SLSCP Regular 72-gon Mathematics II. Problem(s)" based on these.

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