1. ## [SOLVED] Hexnut area

I need to double check something here:

Find the shaded area of the regular hexagonal donut. The apothem and sides of the smaller hexagon are 1/2 as long as the apothem and sides of the larger hexagon, respectively. a = 6.9 cm and r = 8 cm.

The problem is that I get an area of 503 cm^2 and the supposed correct answer is 497 cm^2. Now, this is small enough to perhaps be a rounding problem, but I can't construct the 497 cm^2 solution. Any takers?

-Dan

2. Apparently we're making the same mistake, TQ. I get 502.82.

3. I am getting about 497.

Remember that $A = \frac{pa}{2}$. So we have a 30-60-90 right triangle, and the length of the side of the bigger hexagon is $15.934$. Then $A = 659.6676$. For the smaller one, the length of a side is $7.967$. Then $\frac{pa}{2} = 164.9169$

Thus $\text{desired area} = 659.6676 - 164.9169 \approx 495$ ( I rounded a little bit, if I hadnt it would be 497). You dont need r. Extra information.

4. Aaaah! I got it now.

If we use the 30-60-90 triangle property the length of one side of the hexagon is 8. This gives the A = 497 solution. If we use the Pythagorean theorem to find the length of the side we get 8.08 or so, giving the A = 502 solution.

The problem is that the apothem is an approximation. It should be 6.9282 cm, not 6.9 cm.

Thank you all.
-Dan