Question

Marris decides to bake his parents a cookie in the shape of a regular dodecagon (12‑gon) for their 12-day anniversary.

Answer 1

Answer:

The answer to each question is:

• A.) 403.2 $cm^{2}$
• B.) 100. 8 $cm^{2}$

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 * $\frac{2+\sqrt{3}}{2}$

If we replace the value of the edge, we obtain:

• Apothem = 6 cm * $\frac{2+\sqrt{3}}{2}$
• 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 $cm^{2}$

Then, the area of the dodecagon is 403.2 $cm^{2}$ approximately.

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 $cm^{2}$
• 3 pieces = X

Then:

• X = (3 * 403.2 $cm^{2}$) / 12
• X = 1209.6 $cm^{2}$ / 12
• X = 100. 8 $cm^{2}$

In this form, when the cookie has 3 pieces, its area is 100. 8 $cm^{2}$ approximately.