To find the area of a triangle, we can use the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Step 1: Calculate the area of the first triangular sign.
For the first sign:
- Height = 3 feet
- Base = 2.5 feet
Using the area formula:
\[ \text{Area}_1 = \frac{1}{2} \times 2.5 \times 3 \]
Calculating this:
\[ \text{Area}_1 = \frac{1}{2} \times 7.5 = 3.75 \text{ square feet} \]
Step 2: Calculate the area of the second triangular sign.
For the second sign:
- Height = 2.5 feet
- Base = 3 feet
Using the area formula:
\[ \text{Area}_2 = \frac{1}{2} \times 3 \times 2.5 \]
Calculating this:
\[ \text{Area}_2 = \frac{1}{2} \times 7.5 = 3.75 \text{ square feet} \]
Step 3: Compare the areas.
Now we have both areas:
- \(\text{Area}_1 = 3.75\) square feet
- \(\text{Area}_2 = 3.75\) square feet
Step 4: Calculate the difference in area.
Now we calculate how much larger the first area is compared to the second area:
\[ \text{Difference} = \text{Area}_1 - \text{Area}_2 = 3.75 - 3.75 = 0 \]
Conclusion
The first triangular sign is not larger than the second sign; both signs have the same area of 3.75 square feet.
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