Step-by-step explanation:
With reference to the regular hexagon, from the image above we can see that it is formed by six triangles whose sides are two circle's radii and the hexagon's side. The angle of each of these triangles' vertex that is in the circle center is equal to 360∘6=60∘ and so must be the two other angles formed with the triangle's base to each one of the radii: so these triangles are equilateral.
The apothem divides equally each one of the equilateral triangles in two right triangles whose sides are circle's radius, apothem and half of the hexagon's side. Since the apothem forms a right angle with the hexagon's side and since the hexagon's side forms 60∘ with a circle's radius with an endpoint in common with the hexagon's side, we can determine the side in this fashion:
tan60∘=opposed cathetusadjacent cathetus => √3=Apothemside2 => side=(2√3)Apothem
As already mentioned the area of the regular hexagon is formed by the area of 6 equilateral triangles (for each of these triangle's the base is a hexagon's side and the apothem functions as height) or:
Shexagon=6⋅S△=6(base)(height)2=3(2√3)Apothem⋅Apothem=(6√3)(Apothem)2
=> Shexagon=6×62√3=216
Answer:
Time spend by Adelina at the tutoring session is 30 minutes.
Step-by-step explanation:
Given : In a tutoring session, 
of an hour was spent reviewing math problems and Adelina attended 
of the tutoring session.
We have to find the time Adelina spend at the tutoring session.
We know, 1 hour = 60 minutes.
Total time taken in tutoring session = 
minutes.
also, Adelina attended of the tutoring session that is of 40 minutes.
that is 
minutes.
Thus, time spend by Adelina at the tutoring session is 30 minutes.
Answer:
B: 192pi - 144
Step-by-step explanation:
Area of the sector = (120/360) * pi * r^2
Area of the sector = 1/3 * pi * 24 * 24
Area of the sector = 192 * pi
Now to find the area of the triangle.
The triangle is an isosceles triangle That means two of its sides are equal. They are equal to the radius of the circle, which is 24.
the small angles are equal to
2x + 120 = 180 Subtract 120 from both sides
2x = 60 Divide by 2
x = 60/2
x = 30
The height of the triangle is derived from sin(30) = opposite / hypotenuse
sin(30) = 1/2
hypotenuse = 24
1/2 = opposite / hypotenuse
1/2 = opposite / 24 Multiply both sides by 24
1/2 * 24 = opposite
opposite = 12
The height = 12
r = 24
Area of the triangle = 1/2 * 12 * 24
Area of the triangle = 144
So the area of the shaded area = 192*pi - 144 which looks like B
Answer:
im sorry i dont know but this is for a challenge sorry
Step-by-step explanation:
Answer:
s=15
r=10
Step-by-step explanation:
What we know)
The measure of a line is 180º
If two parrel lines are cut by a transversal, the corresponding angles are congruent (corresponding angles postulate)
What we can figure out)
The angle measuring 3r+3s and 6r+3s are on the same line, so
3r+3s+6r+3s=180
3r+3s and 6r+s are corresponding, so
3r+3s=6r+s
Solve)
Now, we just need to solve the equations.
3r+3s+6r+3s=180 can be condensed into 9r+6s=180 by combining like terms. Then, you can divide by 3 to get 3r+2s=60
3r+3s=6r+s can be turned into 2s=3r by subtracting 3r and s.
So we have 3r+2s=60 and 2s=3r
We can substitute 2s for 3r
2s+2s=60
4s=60
s=15
Then, we can plug s=15 into the equation
2(15)=3r
30=3r
r=10
