https://file.aiquickdraw.com/mathbot/file/172540597100579rfdhhz.jpg

The image shows a trapezium \(ABCD\) where \(AB\) is parallel to \(DC\). The lengths given are \(AB = 7 \text{ cm}\) and \(DC = 21 \text{ cm}\). The problem appears to ask for the length of segment \(XY\), which is a line parallel to the bases \(AB\) and \(DC\).

To solve this, we can use the property that the line segment parallel to the bases in a trapezium divides the trapezium into two similar trapezoids. The length of \(XY\) can be calculated using the formula:

\[
XY = \frac{AB + DC}{2}
\]

Substituting the given values:

\[
XY = \frac{7 \text{ cm} + 21 \text{ cm}}{2} = \frac{28 \text{ cm}}{2} = 14 \text{ cm}
\]

So, the length of \(XY\) is \(14 \text{ cm}\).

Would you like more details or have any questions?

Here are some related questions:

1. How would you calculate \(XY\) if \(AB\) and \(DC\) were given in different units?
2. What is the area of the trapezium \(ABCD\) given the heights?
3. How do you prove that the segments \(XY\) and \(AB\) are parallel?
4. If \(XY\) is extended to meet \(AD\) and \(BC\), how would you find the lengths of those segments?
5. Can you determine the height of trapezium \(ABCD\) if additional information is given?

**Tip:** Remember that in trapeziums, the mid-segment (parallel to both bases) is always the average of the lengths of the two bases.

Given a trapezium ABCD with AB = 7 cm, DC = 21 cm, and XY is parallel to AB and DC. Find the length of XY.

Learn how to find the length of the mid-segment XY in a trapezium where the lengths of the parallel sides AB and DC are given as 7 cm and 21 cm, respectively. This problem involves key geometric concepts and is suitable for students in Grades 6-8.

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