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?