We are given the formula for the area of a trapezium, $A = \frac{1}{2}(a + b)h$, where:

• $a$ and $b$ are the lengths of the parallel sides,
• $h$ is the height (distance between the parallel sides),
• $A$ is the area.

In the diagram:

• $a = 4 \, \text{cm}$,
• $b = 5 \, \text{cm}$,
• $A = 27 \, \text{cm}^2$,
• $h = x$ (which we need to find).

Using the area formula, substitute the given values:

$27 = \frac{1}{2}(4 + 5) \cdot x$

First, simplify the equation:

$27 = \frac{1}{2}(9) \cdot x$

$27 = \frac{9}{2} \cdot x$

Multiply both sides by 2 to eliminate the fraction:

$54 = 9x$

Now, solve for $x$:

$x = \frac{54}{9} = 6$

So, the value of $x$ is 6 cm.

Would you like further clarification or a breakdown of any part of the solution?

Here are 5 related questions for practice:

1. What is the area of a trapezium if the lengths of the parallel sides are 8 cm and 10 cm, and the height is 7 cm?
2. If the area of a trapezium is 40 cm², and the lengths of the parallel sides are 6 cm and 4 cm, what is the height?
3. How does the area of a trapezium change if the height is doubled while keeping the parallel sides constant?
4. If a trapezium has an area of 36 cm², with one parallel side 5 cm and the height 4 cm, what is the length of the other parallel side?
5. What is the relationship between the height and area of a trapezium for fixed lengths of the parallel sides?

Tip: Always ensure the units are consistent (e.g., all in cm or m) when using area formulas.