hi zee-f

3. If a hexagon has a radius (center to point of angle) of 6, what is the side of the hexagon?

3. Ok I need to find the area to get the side. So I know that if I have the radius I can find the area by doing the following : A = r² * N * sin(360/n) / 2

A= 6² * 6 * sin(360/6) / 2 = 93.53074361

I know that area = 3 sqrt(3) / 2 * side² So S= 93.53074361 / 3sqrt(3)/2 which equales 36 So the side of the hexogon = 36

You mean side^2 = 36 so side = √ 36

method perfectly correct, but you've gone the long way to get this. A regular hexagon is made up of 6 equilateral triangles, so, if the radius is 6, so are the sides.

4. If a hexagon has a radius (center to point of angle) of 6, what is the area of the hexagon?

4. A = r² * N * sin(360/n) / 2

A= 6² * 6 * sin(360/6) / 2 = 93.53074361

So the area of the hexagon = 93.53074361

Correct!

5. If a hexagon is resting on a flat side, and has a total height of 18, what is the length of each side of the hexagon?

5. Ok I need to find the area to get the length of each side . If H is 18 that means the apothem equales 9 So that means the area = A^2 * N * tan * (180/n)

area= 9^2 * 6 * tan * (180/6) = 280.59

So I know that the area for a regular hexagon = 3SQRT(3) / 2 multipliyed by S^2

280.59 = 3SQRT(3) /2 * S^2

S^2 = 280.59 / 3SQRT (3) = 81

So the length of each side of the hexagon = 81

This is way too big for H=18. I wonder what went wrong?

area calculation looks ok.

so I think it's the second part that's gone wrong

area = 0.5 x side x side x sin60 x 6

sin60 =√ 3 /2 so that looks good too.

6. If a hexagon is resting on a flat side, and has a total height of 18, what is the area of the hexagon?

6- If H is 18 that means the apothem equales 9 So that means the area = A^2 * N * tan * (180/n)

area= 9^2 * 6 * tan * (180/6) = 280.59

Correct!Bob