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Aimi

Guest

Triginometry & Area of Polygon Help

1. An equilateral triangle with a side of 1 inch

(1/4)(sqrt 3)(1^2)

(1/4)(sqrt 3)

0.433

2. A square with a side of 2 feet  

2*2 = 4

4 feet

3. A regular pentagon with a side of 3 centimeters

360/5 = 72

180 - 72 = 108

108/2 = 54

1/2(1.5) = 0.75 

0.75 x 54 = 40.5

3x40.5= 121.5

121.5 x 5 = 607.5

607.5

4. A regular hexagon with a side of 10 cm

360/6 = 60

180-60 = 120

120/2 = 60

1/2(5) = 2.5

2.5 x 60 = 150

10 x 150 = 1500

1500 x 6 = 9000

9000

I need to use trigonometry in order to calculate 3 and 4, but I'm very confused on where I went wrong. Please help me find a better way to calculate the area

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Triginometry & Area of Polygon Help

hi Aimi

Welcome to the forum.

It is not clear what you are doing to get these answers.  The oft used method is:

(1) Find the centre of the regular polygon and draw out radiating lines to the vertices so that the polygon is divided into n isosceles triangles, where the polygon has n sides.

(2) Calculate the angle at the centre by dividing 360 by n.

(3) Split one isosceles triangle in two equal halves each with a right angle at the base. Calculate one base angle.

(4) Use this to calculate the height of the triangle , half base times TAN(angle)

(5) Calculate the area of one isosceles triangle with 0.5 times base times height.

(6) Multiply by n to get the area of the polygon.

Here's how that works for a pentagon:

(1) n = 5

(2) top angle of one triangle = 360/5 = 72

(3)Base angle = (180 - 72)/2 = 54

(4) height = 1.5 x TAN(54) = 2.06

(5) Area of one triangle =  0.5 x 3 x 2.06

(6)  that answer x 6.

Bob

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