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:
answer is 7
Hope it's help you ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️
Answer:
60
Step-by-step explanation:
What we know:
- ABD is a straight angle, it measures 180 degrees
- Angle CBA + CBD = 180 degrees
- Angle GFH = CBA (they are alternate exterior angles)
Equation:
GFH + CBD = 180
Substitute:
3x + 6x = 180
Add:
3x + 6x = 180
9x = 180
Divide:
9x = 180
/9 /9
x = 20
Substitute:
GFH = 3x
GFH = 3(20)
GFH = 60
m<GFH is 60°
X= 36 I think
Hope this helps
Answer:

Step-by-step explanation:
We are going to apply algebra to solve for the exponential growth
we know that the expression for the exponential formula is

where
a = the amount before measuring growth or decay
= 10,000
r = growth or decay rate = 23%= 0.23
x = number of time intervals that have passed
since this problem is on the growth we are going to replace "b" with (1+r), likewise for decay (1-r)
hence the formula becomes


The expression that will give the population value is
