https://file.aiquickdraw.com/mathbot/file/1726662614864u9hcbstq.jpg

The image you provided shows a trapezium with one base labeled \( 33 \, \text{cm} \), the top side labeled \( 4z \, \text{cm} \), and the height labeled \( 4 \, \text{cm} \). The area of the trapezium is given as \( 114 \, \text{cm}^2 \).

The formula to calculate the area of a trapezium is:

\[
\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
\]

Using the values from the image:
\[
114 = \frac{1}{2} \times (33 + 4z) \times 4
\]

Let's solve this equation for \( z \). 

First, simplifying the equation:
\[
114 = 2 \times (33 + 4z)
\]
\[
114 = 66 + 8z
\]
Now, solve for \( z \):
\[
114 - 66 = 8z
\]
\[
48 = 8z
\]
\[
z = \frac{48}{8} = 6
\]

Thus, \( z = 6 \).

The length of the top side of the trapezium is \( 4z = 4 \times 6 = 24 \, \text{cm} \).

Would you like more details or further clarification on this problem?

Here are some related questions to extend your learning:
1. What is the perimeter of the trapezium when \( z = 6 \)?
2. How would the area change if the height were doubled while keeping the bases the same?
3. If the top side were \( 5z \) cm instead of \( 4z \) cm, how would that affect the value of \( z \)?
4. What would the area be if \( z = 8 \) instead of \( z = 6 \)?
5. How do you find the median (midsegment) of a trapezium and what is its length in this case?

**Tip:** When dealing with a trapezium, always ensure you have both base lengths and the height to calculate the area effectively!

What is the value of z in a trapezium where one base is 33 cm, the top side is 4z cm, the height is 4 cm, and the area is 114 cm²?

In this problem, we solve for z in a trapezium where one base is 33 cm, the top side is 4z cm, the height is 4 cm, and the area is 114 cm². Learn how to apply the area formula for a trapezium and solve a linear equation. Suitable for students in Grades 8-10.

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