SOLUTION: The area of a circle is 89.42 cm2. Which of the following most nearly gives the length of the side of a regular hexagon inscribed in the circle? A. 4.22 cm B. 5.33 cm C. 5.89 c

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Question 1153294: The area of a circle is 89.42 cm2. Which of the following most nearly gives the length of the side of a regular hexagon inscribed in the circle?
A. 4.22 cm
B. 5.33 cm
C. 5.89 cm
D. 6.12 cm
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Untitled-143-300x199.png

From the figure, it is clear that, we can divide the regular hexagon into 6 identical equilateral triangles.
We take one triangle OAB, with O+as the center of the hexagon or circle, & AB+as one side of the hexagon.
Let M+be mid-point of AB, OM would be the perpendicular bisector of AB, angle AOM+=+30°
Then in right angled triangle OAM, side is a
tan%28x%29+=+tan%2830%29+=+1%2Fsqrt%283%29
So, a%2F2r+=+1%2Fsqrt%283%29
Therefore, r+=+%28a%2Asqrt%283%29%29%2F2
Area of circle is,
A+=pi%2Ar%5E2
A+=pi%2A%28%28a%2Asqrt%283%29%29%2F2%29%5E2
if given that the area of a circle is 89.42cm%5E2, we have
89.42cm%5E2=%283%2Api%2F4%29a%5E2
89.42cm%5E2+=2.356a%5E2
a%5E2=89.42cm%5E2%2F2.356
a%5E2=37.95cm%5E2
a=6.16cm
so,
D. 6.12 cm -> should be 6.16cm



Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
The area of a circle is 89.42 cm2.
Which of the following most nearly gives the length of the side of a regular hexagon inscribed in the circle?
A. 4.22 cm
B. 5.33 cm
C. 5.89 cm
D. 6.12 cm
~~~~~~~~~~~~~~~~~ 


The length of the side of a regular hexagon inscribed in a circle is equal to the radius of the circle.


Find the radius of the given circle from the given area


    pi%2Ar%5E2 = 89.42

    r^2 = 89.42%2F3.14 = 28.477

    r = sqrt%2828.477%29 = 5.34  (approximately).


ANSWER.  The side length of a regular hexagon inscribed in the given circle is 5.34 cm.

         The closest optional answer is B.


Solved, explained and answered. And completed.

----------------

Be aware !   Tutor @MathLover1 misread the problem,

                    So her solution and the answer are  IRRELEVANT.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a circle is 89.42 cm2. Which of the following most nearly gives the length of the side of a regular hexagon inscribed in the circle?
A. 4.22 cm
B. 5.33 cm
C. 5.89 cm
D. 6.12 cm
As stated, TOTALLY IGNORE the person who claims to LOVE MATH.

Area of THIS circle: 89.42 cm2

Area of ANY circle: πr2

We then get: πr2 = 89.42 

matrix%281%2C3%2C+r%5E2%2C+%22=%22%2C+89.42%2Fpi%29

r, or 

The RADIUS of the circle is the same length as the length of ANY one of the ISOSCELES sides of the 6 triangles of the INSCRIBED REGULAR HEXAGON!