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Solving the area of a Dectagon

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danny montana

on 2 March 2014

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Transcript of Solving the area of a Dectagon

Solving the area of a Decagon
Step 1
first we know the side length of the decagon is 10.
Step 2
finding the angle
Step 3
Step 4
putting the info together
Step 5
finding the area
since we know this is ten we can find our perimeter.
Since we can find our perimeter
we have to multiply 10 by the number of sides there are which are 10. so our answer would be 100.
Perimeter would be 100
10
first we are going
to find the individual angle measurement
to do that we're
going to do this,
(10-2)180/10
10-2=8
(8)180=1440
1440/10=144
since we know the angle measurement is 144
we can make a little triangle
5
90
72
144/2=72
10/2=5
finding the apothem using Soh Cah Toa
90
72
5
90
72
5
were going to us Tangent to find the apothem
so the equation will look like this.
Tan(72)= x/5
the final step to
finding the apothem
is solving the equation
Tan(72)= x/5
5Tan(72)=x
x=15.38841769
15.38841769
5
90
72
Apothem=15.38841769
Perimeter=100
To find the area we are going to use the
this fourmula A=1/2AP
Now we are going to plug in our info
A=1/2(15.38841769*100)
Apothem
Perimeter
To solve multiply
15.38841769*100=1538.841769
No we plug that in the equation
A=1/2(1538.841769)=769.42 units ²
so the area fo the decagon is
769.42 units²
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