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:
(x, y ) → (x + 6, y + 12 )
Step-by-step explanation:
We require to determine the horizontal and vertical shift to go from one of the points on the line to the corresponding point on the image
Consider point V with x- coordinate - 8 and y- coordinate - 2
The corresponding point is V'
with x- coordinate - 2 and y- coordinate 10
Thus V → V' is 6 units right in the horizontal direction and 12 units up in the vertical direction.
These are the same shifts for W → W'
Thus the translation rule is
(x, y ) → (x + 6, y + 12 )
Answer:
I did learn this before I'm not sure, but I think the answer is X x 10 = Y because on the chart for example X= 1 and Y= 10 so whatever number is on Y is basically X multiplied by 10. I hope this helps!
I believe so ,,,,,,,,,,,,,,,,,,,,
The answers are as follows:
Box 1) D
Box 2) .02D
Box 3) D + .02D
