What radius of a circle is required to inscribe a regular hexagon with an area of 64.95 cm2 and an apothem of 4.33 cm? A) 4 cm B) 5 cm C) 6 cm D) 7 cm
Question
Answer:
we know thatthe regular hexagon can be divided into 6 equilateral triangles
[area of regular hexagon]=6*[area of one equilateral triangle]
area of one equilateral triangle=b*h/2
b=length side of a regular hexagon
h=apothem-----> 4.33 cm
area of one equilateral triangle=b*(4.33)/2------> 2.165*b cm²
[area of regular hexagon]=6*[area of one equilateral triangle]
[area of regular hexagon]=64.95 cm²
64.95=6*[2.165*b]--------> b=64.95/[6*2.165]-----> b=5 cm
the length side of the regular hexagon is equal to the radius of the circle
therefore
the radius required to inscribe a regular hexagon is 5 cm
the answer is
5 cm
solved
general
8 months ago
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