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We are given that the two trapeziums, A and B, are similar, meaning their corresponding dimensions have the same ratio. We need to calculate the area of trapezium B, and if the answer is a decimal, it should be rounded to one decimal place.

### Step 1: Determine the Scale Factor
To start, we find the scale factor between trapezium A and trapezium B. The bases of the trapeziums are given as:
- Trapezium A: 16 cm
- Trapezium B: 30 cm

The scale factor between trapezium B and trapezium A is:
\[
\text{Scale Factor} = \frac{\text{Base of B}}{\text{Base of A}} = \frac{30}{16} = 1.875
\]

### Step 2: Use the Scale Factor to Find the Area of Trapezium B
Since the trapeziums are similar, the ratio of their areas is the square of the scale factor. Therefore, the area of trapezium B can be calculated as follows:
\[
\text{Area of B} = (\text{Scale Factor})^2 \times \text{Area of A}
\]
Substituting the values:
\[
\text{Area of B} = (1.875)^2 \times 98 = 3.515625 \times 98 = 344.53 \, \text{cm}^2
\]

### Final Answer:
The area of trapezium B is approximately **344.5 cm²** (rounded to 1 decimal place).

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Would you like further details or have any questions? Here are 5 related questions to explore:

1. How do you calculate the area of a trapezium in general?
2. What other dimensions could you use to verify the similarity of these trapeziums?
3. What would the height of trapezium B be, given this scale factor?
4. How would the result change if the trapeziums were not similar?
5. How can we use the perimeter of trapezium B to cross-check the calculations?

**Tip:** Remember that for similar figures, areas scale by the square of the linear dimensions' scale factor!

These two trapeziums are similar. Calculate the area of trapezium B. If your answer is a decimal, give it to 1 d.p.

Learn how to calculate the area of trapezium B using the similarity of trapeziums A and B. This problem involves calculating the scale factor and using it to find the area of the larger trapezium. Suitable for students in Grades 8-10.

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