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To calculate the area of trapezium \( H \), let's analyze the given diagram step by step.

1. The trapezium consists of a larger triangle (colored pink, representing the area of \( H \)) and a smaller triangle (colored blue) with a given area of \( 30 \, \text{cm}^2 \).

2. The total height of both triangles combined is \( 27 + 9 = 36 \, \text{cm} \). The smaller triangle has a height of \( 9 \, \text{cm} \).

3. The formula for the area of a triangle is:
   \[
   \text{Area of a triangle} = \frac{1}{2} \times \text{base} \times \text{height}
   \]

4. From the smaller triangle, we can determine its base since the area and height are given:
   \[
   30 = \frac{1}{2} \times \text{base} \times 9
   \]
   Solving for the base:
   \[
   \text{base} = \frac{30 \times 2}{9} = \frac{60}{9} = 6.67 \, \text{cm}
   \]

5. Since the trapezium shares the same base as the larger triangle, the base of trapezium \( H \) is \( 6.67 \, \text{cm} \), and its height is \( 27 \, \text{cm} \).

6. Using the area formula for a triangle again to find the area of trapezium \( H \):
   \[
   \text{Area of trapezium } H = \frac{1}{2} \times 6.67 \times 27 = 90 \, \text{cm}^2
   \]

Therefore, the area of trapezium \( H \) is \( 90 \, \text{cm}^2 \).

Would you like a detailed breakdown of any step? Let me know if you have any further questions!

Here are 5 related questions:
1. How do you calculate the area of a trapezium if both bases are known?
2. What is the relationship between the area of triangles and trapeziums?
3. How can you calculate the height of a triangle given its area and base?
4. How would the problem change if the base of the trapezium were doubled?
5. Can you calculate the perimeter of trapezium \( H \) given the current information?

**Tip:** When working with geometric shapes, always check if they share common sides or dimensions to simplify your calculations.

Work out the area of trapezium H. If your answer is a decimal, give it to 1 decimal place.

Learn how to calculate the area of trapezium H by using the given area of a smaller triangle. This step-by-step explanation covers important geometry concepts, including triangle and trapezium areas. Suitable for Grades 6-8.

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