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 answer is
Step-by-step explanation:
To find an equation of a line when given the slope and a point we use the formula
From the question we have
We have the final answer as
<h3>y = -2x</h3>
Hope this helps you
I hope this helps, i got it from a cheat sheet online
Answer:
Kevin will take 3 hours to make all pieces.
Step-by-step explanation:
Kevin is building a large model of a soccer ball which is made of 20 hexagons and 12 pentagons.
Time taken by Kevin to measure and cut each hexagon = 6 minutes
Therefore, time taken to make 20 hexagons = 6×20 = 120 minutes
Similarly time taken by him to measure and cut a pentagon = 5 minutes
So, time taken to make 12 pentagons = 12×5 = 60 minutes
Total time taken to measure and cut 12 pentagons and 20 hexagons = 60+120 = 180 minutes
Therefore, Kevin will take 180 minutes or 3 hours to make all pieces.
