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We are given two similar trapeziums, F and G, and asked to calculate the area of trapezium G. The dimensions of trapezium F and its area are provided, along with the base lengths of both trapeziums.

### Given information:
- Trapezium F:
  - Area = \( 70 \, \text{cm}^2 \)
  - Base 1 = \( 16 \, \text{cm} \)
  - Height = \( 5 \, \text{cm} \)
  
- Trapezium G:
  - Base 1 = \( 30 \, \text{cm} \)

### Since the trapeziums are similar:
The ratio of areas of two similar figures is proportional to the square of the ratio of their corresponding linear dimensions.

Let's calculate the ratio of the corresponding linear dimensions first:
\[
\text{Ratio of linear dimensions} = \frac{\text{Base of G}}{\text{Base of F}} = \frac{30 \, \text{cm}}{16 \, \text{cm}} = 1.875
\]

The area ratio will be the square of the linear ratio:
\[
\text{Area ratio} = (1.875)^2 = 3.515625
\]

Now, using the area ratio, we can find the area of trapezium G:
\[
\text{Area of G} = \text{Area of F} \times \text{Area ratio} = 70 \, \text{cm}^2 \times 3.515625 = 246.09375 \, \text{cm}^2
\]

Rounding this to 1 decimal place:
\[
\text{Area of G} = 246.1 \, \text{cm}^2
\]

Thus, the area of trapezium G is \( 246.1 \, \text{cm}^2 \).

Would you like further details or have any questions? Here are some related questions:

1. How would the height of trapezium G be determined based on this information?
2. If the bases of trapezium F and G had different ratios, how would that affect the calculation?
3. Can you generalize this method for any pair of similar shapes?
4. How does knowing that the trapeziums are similar help simplify the problem?
5. How would you calculate the area if the trapezium G's height was provided?

**Tip:** When working with similar shapes, always remember that the ratio of areas is the square of the ratio of corresponding linear dimensions.

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

Learn how to calculate the area of trapezium G based on the similarity of two trapeziums F and G. This problem involves calculating the area ratio and applying geometric principles of similarity. Suitable for students in Grades 8-10.

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