We know that
<span>the regular hexagon can be divided into 6 equilateral triangles
</span>
area of one equilateral triangle=s²*√3/4
for s=3 in
area of one equilateral triangle=9*√3/4 in²
area of a circle=pi*r²
in this problem the radius is equal to the side of a regular hexagon
r=3 in
area of the circle=pi*3²-----> 9*pi in²
we divide that area into 6 equal parts------> 9*pi/6----> 3*pi/2 in²
the area of a segment formed by a side of the hexagon and the circle is equal to <span>1/6 of the area of the circle minus the area of 1 equilateral triangle
</span>so
[ (3/2)*pi in²-(9/4)*√3 in²]
the answer is
[ (3/2)*pi in²-(9/4)*√3 in²]
You can do that by simply measuring the main angle and then measuring each of the two angles. If you bisected the angle correctly, you will find that each of the two angles is equal to half the original.
You can measure the angle by following these steps:
1- Place the straightedge on the base of the angle.
2- Slide the protractor over it until the vertex of the angle is at the zero of the protractor.
3- Measure the angle.
We can figure out how long Michael's trip took by realizing that 30 mph is 3 times 10 mph. Because of this, the trip home will take 1/3 the amount of time it took to go up the hill. This makes the equation 24 + 8 = 32 minutes for the whole trip.
Now we need to figure out how long the trip was. We can do this by multiplying 10 minutes by 24/60, which equals 4. This means that Michael went 4 miles there, and 4 miles back. So Michael went a total of 8 miles.
Now we know that Michael went 8 miles in 32 minutes. Now, we multiply 8 by 60/32. This gives us 15, so Michael went 15 miles per hour on average in the trip.
