https://file.aiquickdraw.com/mathbot/file/17269082936309wh13nb2.jpg

Let's analyze the trapezium and the given dimensions from the image you shared:

- The trapezium has one pair of parallel sides: a shorter base of **6 meters** and a longer base of **10 meters**.
- The height (distance between the parallel sides) is **5 meters**.

### Part (a): Finding the base length of each triangle on the sides

The trapezium can be divided into a rectangle and two right-angled triangles on the sides, by drawing perpendicular lines from the endpoints of the shorter base to the longer base.

1. The length of the shorter base (top side of the trapezium) is **6 meters**, and the longer base (bottom side) is **10 meters**.
2. The difference between these two bases is \( 10 - 6 = 4 \) meters. This difference is distributed equally between the two triangles on the sides.

Therefore, each of the two right-angled triangles will have a base of \( \frac{4}{2} = 2 \) meters.

#### Justification:
- Since the difference between the two parallel sides is 4 meters, and this difference is symmetrically divided between the two triangles, the base of each triangle must be 2 meters.

Let me know if you need further details!

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Here are some related questions for deeper understanding:

1. What is the area of the trapezium using the dimensions provided?
2. How would you find the hypotenuse of each triangle?
3. How can the Pythagorean theorem be applied to the triangles in this trapezium?
4. If the height were increased, how would it affect the area of the trapezium?
5. Can you find the angles in the right-angled triangles on the sides?

**Tip**: When dealing with geometric shapes, breaking complex shapes into simpler ones (like triangles and rectangles) often simplifies calculations.

For the trapezium shown in the image, is it possible to find the base length of each triangle on the sides? Justify your answer.

Learn how to calculate the base lengths of triangles formed on the sides of a trapezium. This problem involves key geometric concepts such as the properties of trapeziums and the geometry of right-angled triangles. Suitable for Grades 7-9 students.

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