Question

A triangular road sign has a height of 3 feet and a base of 2.5 feet. how much larger in area is this sign than one with a height of 2.5 feet and a base of 3 feet

SHOW WORK

Answer 1

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**.