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To calculate the area of trapezium H, we can use the formula for the area of a trapezium:

\[
\text{Area} = \frac{1}{2} \times (a + b) \times h
\]

Where:
- \( a \) and \( b \) are the lengths of the parallel sides,
- \( h \) is the height (the perpendicular distance between the parallel sides).

From the image:
- The height of the trapezium \( h \) is the same as the total vertical height, which is \( 27 \, \text{cm} + 9 \, \text{cm} = 36 \, \text{cm} \).
- One of the bases (parallel sides) is given by the length of the smaller blue triangle's base, but this is not directly given.

To calculate the other information:
- The area of the blue triangle is given as \( 30 \, \text{cm}^2 \).
- The height of the blue triangle is \( 9 \, \text{cm} \), so using the formula for the area of a triangle (\( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \)):

\[
30 = \frac{1}{2} \times \text{base} \times 9
\]

Solving for the base of the triangle:

\[
\text{base} = \frac{30 \times 2}{9} = \frac{60}{9} = 6.67 \, \text{cm}
\]

Now, using this, the smaller base of the trapezium is \( 6.67 \, \text{cm} \), and the total length of the larger base of trapezium H is unknown, but we will calculate it from the remaining parts of the problem or given hints.

Would you like to proceed with further clarifications, or should I assume any missing lengths?

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 using geometric formulas for trapeziums and triangles. This problem includes step-by-step guidance on using the area formulas with the given dimensions. Suitable for students in Grades 8-10.

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