The area of a polygon is given by the formula Area = ap/2 where a is the length of the apothem and p is the perimeter. The apothem is a line from the center of the polygon perpendicular to a side.
Depending on the formula you know, you can find the length of a side in 1 of 2 ways.
The first way uses a triangle. Using the radius of the polygon you can create 8 congruent triangles. The center angle will be 360 / 8 = 45 and two side lengths of 20. You can find the length of the base using the law of cosines.
c^2 = 20^2 + 20^2 - 2(20)(20)(cos 45)
c^2 = 400 + 400 - 800(cos 45)
c^2 = 800 - 800(cos 45)
c = sqrt(800 - 800(cos 45)
c = 15.31
The second way is to use this formula:
r = s / (2 sin(180 / n))
20 = s / (2 sin(180/8)
(20)(2)sin(22.5) = s
(40)sin(22.5) = s
s = 15.31
We need to calculate the perimeter. As there are 8 sides (8)(15.31) = 122.48
Now we need to calculate the apothem using
a = S / (2 tan (180 / n)
a = 15.31 / (2 tan (180 / 8))
a = 18.48
Now solve for the area
Area = ap/2
Area = (18.48)(122.48)/2
Area = 1131.72
perimeter = 122.48
area = 1131.72
Answer:
The margin of error (E) 
Step-by-step explanation:
Given,
mean 
standard deviation 
sample size 
Critical value ![=\frac{z_\alpha}{2}\quad \quad\quad[\because\;\alpha=1-\text{confidence interval}]](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bz_%5Calpha%7D%7B2%7D%5Cquad%20%5Cquad%5Cquad%5B%5Cbecause%5C%3B%5Calpha%3D1-%5Ctext%7Bconfidence%20interval%7D%5D)
Critical value 
The margin of error (E) 
Hence, The margin of error (E)
Complete question is attached in below.
Answer:
8x - 20
Step-by-step explanation:
6(2x - 3) - 2(2x + 1)
Distribute
6(2x) -6( 3) - 2(2x) -2( 1)
12x -18 -4x -2
Combine like terms
12x -4x -18 -2
8x-20
Answer:
38=7x-y
Step-by-step explanation:
standard form= Ax+By+C
(y-3=7(x-5))
(y-3=7x-35)+3 to both sides
(y=7x-38) +38 to both sides
(y+38=7x) -y to both sides
38=7x-y
you have to move the 38 and y because if you moved the x value, than A becomes negative and it can't be in standard form
