Question

A yield sign is a regular triangle. Its apothem measures 10.4 inches. What is the area of the sign to the nearest whole number?(1 point) which answer is correct so I can get a 100
The area of the yield sign is approximately
in.2
.
Remaining Attempts : 1View prev

Answer 1

To find the area of a regular triangle using the apothem, you can use the following formula:

\[
\text{Area} = \text{Apothem} \times \text{Perimeter} \div 2
\]

1. First, we need to relate the apothem to the side length of the triangle. For a regular triangle (equilateral triangle), the relationship between the side length \( s \) and the apothem \( a \) is given by:

\[
a = \frac{s \sqrt{3}}{6}
\]

We can rearrange this to find \( s \):

\[
s = \frac{6a}{\sqrt{3}} = 2\sqrt{3}a
\]

For \( a = 10.4 \) inches:

\[
s = 2\sqrt{3} \times 10.4 \approx 36.0 \text{ inches (approximately)}
\]

2. Next, we need to find the perimeter \( P \) of the triangle:

\[
P = 3s \approx 3 \times 36.0 \approx 108.0 \text{ inches}
\]

3. Now, we can find the area:

\[
\text{Area} = \frac{10.4 \times 108.0}{2} \approx 561.6 \text{ square inches}
\]

Rounding to the nearest whole number, the area of the yield sign is approximately:

\[
\text{Area} \approx 562 \text{ square inches}
\]

Thus, the area of the yield sign is approximately **562 in²**.