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To solve this problem, we need to compare the areas of Triangle B and Triangle F.

### Step 1: Formula for area of a triangle
The area of a triangle is given by:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

### Step 2: Calculating the area of Triangle B
For Triangle B, the base is \( \frac{3}{2} \) and the height is 2. So, the area is:
\[
\text{Area of Triangle B} = \frac{1}{2} \times \frac{3}{2} \times 2 = \frac{1}{2} \times 3 = 1.5
\]

### Step 3: Calculating the area of Triangle F
For Triangle F, the base is 6 and the height is 8. So, the area is:
\[
\text{Area of Triangle F} = \frac{1}{2} \times 6 \times 8 = \frac{1}{2} \times 48 = 24
\]

### Step 4: Finding the ratio of areas
We need to determine how many times larger the area of Triangle F is compared to Triangle B:
\[
\text{Ratio} = \frac{\text{Area of Triangle F}}{\text{Area of Triangle B}} = \frac{24}{1.5} = 16
\]

Thus, the area of Triangle F is 16 times larger than the area of Triangle B.

Would you like more details on any part of the explanation? Here are 5 related questions to explore:

1. How does scaling of triangles affect their areas?
2. What are the properties of similar triangles?
3. Can we determine the ratio of sides between two triangles directly from the areas?
4. How would the result change if we scaled the triangles by a different factor?
5. How can we calculate the area of a triangle if only the lengths of all three sides are given?

**Tip**: The ratio of areas of two similar triangles is the square of the ratio of their corresponding sides.

For the pair of triangles listed below, the area of the second triangle is how many times larger than the area of the first? Triangle B and Triangle F.

In this example, we calculate how many times larger the area of Triangle F is compared to Triangle B. Using the formula for the area of a triangle and the scaling theorem for similar triangles, we determine that the area of Triangle F is 16 times larger than the area of Triangle B. Learn the key steps involved in solving this geometry problem.

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