Answer:
389.1 units² (nearest tenth)
Step-by-step explanation:
<u>Regular polygon</u>: all side lengths are equal, all interior angles are equal.
<u>Apothem</u>: a line drawn from the center of any polygon to the midpoint of one of the sides
<u>Radius</u>: a line drawn from the center of the polygon to a vertex.
Therefore, we have been given the apothem of this regular dodecagon.
<h3><u>Formulae</u></h3>
![\textsf{Area of a regular polygon}=\dfrac{n\:l\:a}{2}](https://tex.z-dn.net/?f=%5Ctextsf%7BArea%20of%20a%20regular%20polygon%7D%3D%5Cdfrac%7Bn%5C%3Al%5C%3Aa%7D%7B2%7D)
where:
- n = number of sides
- l = length of one side
- a = apothem (the line drawn from the center of any polygon to the midpoint of one of the sides)
![\textsf{Length of apothem (a)}=\dfrac{l}{2 \tan\left(\frac{180^{\circ}}{n}\right)}](https://tex.z-dn.net/?f=%5Ctextsf%7BLength%20of%20apothem%20%28a%29%7D%3D%5Cdfrac%7Bl%7D%7B2%20%5Ctan%5Cleft%28%5Cfrac%7B180%5E%7B%5Ccirc%7D%7D%7Bn%7D%5Cright%29%7D)
where:
- l = length of one side
- n = number of sides
<h3><u>Solution</u></h3>
First, calculate the length of one side of the regular dodecagon by substituting a = 11 and n = 12 into the apothem formula:
![\implies 11=\dfrac{l}{2 \tan\left(\frac{180^{\circ}}{12}\right)}](https://tex.z-dn.net/?f=%5Cimplies%2011%3D%5Cdfrac%7Bl%7D%7B2%20%5Ctan%5Cleft%28%5Cfrac%7B180%5E%7B%5Ccirc%7D%7D%7B12%7D%5Cright%29%7D)
![\implies l=11 \cdot 2 \tan\left(\frac{180^{\circ}}{12}\right)](https://tex.z-dn.net/?f=%5Cimplies%20l%3D11%20%5Ccdot%202%20%5Ctan%5Cleft%28%5Cfrac%7B180%5E%7B%5Ccirc%7D%7D%7B12%7D%5Cright%29)
![\implies l=44-22\sqrt{3}](https://tex.z-dn.net/?f=%5Cimplies%20l%3D44-22%5Csqrt%7B3%7D)
Now substitute n = 12, the found value of l, and a = 11 into the area formula:
![\implies \textsf{Area}=\dfrac{12(44-22\sqrt{3})(11)}{2}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctextsf%7BArea%7D%3D%5Cdfrac%7B12%2844-22%5Csqrt%7B3%7D%29%2811%29%7D%7B2%7D)
![\implies \textsf{Area}=389.0622274...](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctextsf%7BArea%7D%3D389.0622274...)
![\implies \textsf{Area}=389.1\: \sf units^2 \: (nearest\:tenth)](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctextsf%7BArea%7D%3D389.1%5C%3A%20%5Csf%20units%5E2%20%5C%3A%20%28nearest%5C%3Atenth%29)
1) 52 + 33= 85
2) 26 + 42 = 68 or 26 - 42 = - 16
3) 72 - 2015 = =1943
4) 32 x 22 = 704
Answer:
Step-by-step explanation:
Use the quadratic formula first; find the roots, and then write the factors based upon the roots. Here, a = 4, b = -8 and c = -5. Thus, the discriminant b^2 - 4ac is (-8)^2 - 4(4)(-5), or 64 + 80, or 144.
Thus, we have:
-(-8) ± √144 8 ± 12
x = --------------------- = -------------- = 5/2 and x = -1/2
2(4) 8
If x = 5/2 is a root, then (2x - 5) is a factor.
If x = -1/2 is a root, then (2x + 1) is the other factor.
or
Answer:
I believe it is 4.
Step-by-step explanation:
If 3 times 2 equals then add 4 which then would 10. hopefully I am not dumb and did not understand this. I have 5 IQ. :)