Answer:
The answer to each question is:
- A.) 403.2
- B.) 100. 8
Step-by-step explanation:
A.) To obtain the area of the dodecagon, you can use the next formula:
- Area of a dodecagon = 6 * apothem * edge
In the exercise, we have the edge (6 cm), but, to find the apothem of a dodecagon, that is the distance between the center of the polygon, and the middle point of each side, you can use the next formula:
- Apothem = Edge *
![\frac{2+\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%2B%5Csqrt%7B3%7D%7D%7B2%7D)
If we replace the value of the edge, we obtain:
- Apothem = 6 cm *
![\frac{2+\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%2B%5Csqrt%7B3%7D%7D%7B2%7D)
- Apothem = 11.2 cm (approximately).
With this data, we can find the area:
- Area of a dodecagon = 6 * apothem * edge
- Area of a dodecagon = 6 * 11.2 cm * 6 cm
- Area of a dodecagon = 403.2
![cm^{2}](https://tex.z-dn.net/?f=cm%5E%7B2%7D)
Then,<u> the area of the dodecagon is 403.2 </u>
<u> approximately</u>.
B.) As the area obtained is for 12 pieces, when the parents ate 9 pieces, just left 3 pieces, with these values you can make a rule of three.
If:
- 12 pieces = 403.2
![cm^{2}](https://tex.z-dn.net/?f=cm%5E%7B2%7D)
- 3 pieces = X
Then:
- X = (3 * 403.2
) / 12 - X = 1209.6
/ 12 - X = 100. 8
In this form, <u>when the cookie has 3 pieces, its area is 100. 8 </u>
<u> approximately</u>.