Question

A regular hexagon is inscribed in a circle. If the difference in their areas is 24m squared, what is the radius of the circle?

Answer 1

Draw a picture and see if you can come up with a formula for area of that hexagon and circle. Then subtract the area of the hexagon from the circle to get all that area leftover and it should equal 24, so you can solve for your radius.

Answer 2

Okay. I will try that. Thank you!

Answer 3

Yeah if you have trouble, put how far you get and I'll help you figure it out. =)

Answer 4

Okay!

Answer 5

The hexagon's area is made up of 6 equilateral triangles of side r, where r is the radius of the circle. The area of each triangle is: 1/2 * r * r * sin(60) = sqrt(3)/4 * r^2. Six such triangles will have an area of 6 * sqrt(3)/4 * r^2 = 3/2 * sqrt(3) * r^2

Area of the hexagon = 3/2 * sqrt(3) * r^2
Area of the circle = pi * r^2

Take the difference, equate it to 24m and solve for r.

Answer 6

Kainui I tried to do that and I haven't had much luck. do you have any suggestion or help?

Answer 7

Area of the circle - Area of the hexagon = pi * r^2 - 3/2 * sqrt(3) * r^2 =
r^2 * (pi - 3/2 * sqrt(3)) = 24
r^2 * 0.54352 = 24
r^2 = 24 / 0.54352
r = 6.645m

Answer 8

Thank you so much!!

Answer 9

Round the radius to the number of decimal places they are looking for.
one decimal: 6.6
two decimals: 6.65
etc.