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

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)   (Show Source): You can put this solution on YOUR website!

From the figure, it is clear that, we can divide the regular hexagon into 6 identical equilateral triangles.
We take one triangle , with as the center of the hexagon or circle, & as one side of the hexagon.
Let be mid-point of , would be the perpendicular bisector of , angle °
Then in right angled triangle , side is

So,
Therefore,
Area of circle is,

if given that the area of a circle is , we have

so,
D. 6.12 cm -> should be

Answer by ikleyn(52781)   (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 = 89.42 r^2 = = 28.477 r = = 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)   (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

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!
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