7.2 percent of the area of the original hexagon was removed
The area of hexagon is the region that lies within the sides of the hexagon. A hexagon is a two-dimensional shape that has 6 sides, 6 angles, and, 9 diagonals, and the sum of its interior angles is 720°
Area of the hexagon = (3√3 s2)/2, where 's' is the length of the side of the hexagon.
Her, We have
Rationalize the denominator to get
The area of the hexagon is and the dodecagon is
The deleted area is percent
Formula used:
Area = (3√3 s2)/2
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Because it is always that many numbers away from the number 0
<u>Part a)</u> if a page is reduced to 80%, what percent enlargement is needed to return it to its original size?
Let
x---------> the percent enlargement
we know that
the original size is the 100%
so
x*80%=100%
x=(100%/80%)
x=1.25--------> 1.25=(125/100)=125%
therefore
<u>the answer Part a) is</u>
the percent enlargement is 125%
<u>Part b)</u> Estimate the number of times in succession that a page must be copied to make the final copy less than 15% of the size of the original
we know that
A photocopy machine can reduce copies to 80% of their original size
so
Copy N 1
0.80*100%=80%
Copy N 2
0.80*80%=64%
Copy N 3
0.80*64%=51.2%
Copy N 4
0.80*51.2%=40.96%
Copy N 5
0.80*40.96%=32.77%
Copy N 6
0.80*32.77%=26.21%
Copy N 7
0.80*26.21%=20.97%
Copy N 8
0.80*20.97%=16.78%
Copy N 9
0.80*16.78%=13.42%-------------> 13.42% < 15%
therefore
<u>the answer Part b) is</u>
the number of times in succession is 9
89+30=119 180-119=61 degrees
The third angle is 61