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) which answer is correct so I can get a 100
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) given the length of a side, we can use the following formula for the area \( A \) of a regular dodecagon with side length \( s \):
\[
A = 3 \times s^2
\]
Here, \( s \) is the length of a side of the dodecagon.
Given that the side length \( s = 5.5 \) inches, we can plug this value into the formula:
\[
A = 3 \times (5.5)^2
\]
Calculating \( (5.5)^2 \):
\[
(5.5)^2 = 30.25
\]
Now, substituting this back into the area formula:
\[
A = 3 \times 30.25 = 90.75
\]
Rounding \( 90.75 \) to the nearest tenth, we get:
\[
A \approx 90.8 \text{ square inches}
\]
Therefore, the clock's area is approximately **90.8 square inches**.
\[
A = 3 \times s^2
\]
Here, \( s \) is the length of a side of the dodecagon.
Given that the side length \( s = 5.5 \) inches, we can plug this value into the formula:
\[
A = 3 \times (5.5)^2
\]
Calculating \( (5.5)^2 \):
\[
(5.5)^2 = 30.25
\]
Now, substituting this back into the area formula:
\[
A = 3 \times 30.25 = 90.75
\]
Rounding \( 90.75 \) to the nearest tenth, we get:
\[
A \approx 90.8 \text{ square inches}
\]
Therefore, the clock's area is approximately **90.8 square inches**.