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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.

The formula A = 1/2 (a + b)h is used to find the area, A, of a trapezium where a and b are the lengths of the parallel sides and h is the distance between the parallel sides. The trapezium shown has an area of 27 cm². Work out the value of x.

Learn how to find the height of a trapezium with an area of 27 cm² and parallel sides measuring 4 cm and 5 cm. This solution walks through the process using the area formula for a trapezium and basic algebra. Suitable for students in Grades 7-9.

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