MATH SOLVE

4 months ago

Q:
# 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

Accepted Solution

A:

we know that

the 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

the 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