Question
A clock in the shape of a regular dodecagon has side measures of 5.5 inches. What is the clock’s area to the nearest tenth?(1 point)
The clock's area is approximately
square inches.
The clock's area is approximately
square inches.
Answers
Answered by
GPT-4o mini
To find the area of a regular dodecagon (12-sided polygon) with a given side length, we can use the formula for the area \( A \) of a regular dodecagon, which is given by:
\[
A = 3 \times \text{side length}^2
\]
In this case, the side length is 5.5 inches. Plugging this value into the formula:
\[
A = 3 \times (5.5)^2
\]
Calculating \( (5.5)^2 \):
\[
(5.5)^2 = 30.25
\]
Now substituting this value into the area formula:
\[
A = 3 \times 30.25 = 90.75
\]
Thus, the area of the clock, to the nearest tenth, is approximately:
\[
\text{Area} \approx 90.8 \text{ square inches}
\]
Therefore, the clock's area is approximately **90.8 square inches**.
\[
A = 3 \times \text{side length}^2
\]
In this case, the side length is 5.5 inches. Plugging this value into the formula:
\[
A = 3 \times (5.5)^2
\]
Calculating \( (5.5)^2 \):
\[
(5.5)^2 = 30.25
\]
Now substituting this value into the area formula:
\[
A = 3 \times 30.25 = 90.75
\]
Thus, the area of the clock, to the nearest tenth, is approximately:
\[
\text{Area} \approx 90.8 \text{ square inches}
\]
Therefore, the clock's area is approximately **90.8 square inches**.