The question asks to find the area of a trapezium (trapezoid in US terms) using the given dimensions and breaking it into simpler shapes—a rectangle and triangles.

Given information:

• One of the parallel sides (top) is 6 m.
• The other parallel side (bottom) is 10 m.
• The height (distance between the parallel sides) is 5 m.

Steps to break the trapezium into simpler shapes:

1. Identify the rectangle: The top part of the trapezium is a rectangle with width 6 m (the length of the top parallel side) and height 5 m.

   • Area of the rectangle = width × height = $6 \, \text{m} \times 5 \, \text{m} = 30 \, \text{m}^2$.

2. Identify the triangles: On either side of the rectangle, there are two right triangles.

   • The total base of the trapezium is 10 m, and the width of the rectangle is 6 m, so the combined base of the two triangles is $10 \, \text{m} - 6 \, \text{m} = 4 \, \text{m}$.

   • Since there are two identical triangles, each triangle has a base of $4 \, \text{m} / 2 = 2 \, \text{m}$.

   • The height of each triangle is the same as the height of the trapezium, 5 m.

   • Area of each triangle = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \, \text{m} \times 5 \, \text{m} = 5 \, \text{m}^2$.

3. Total area of the trapezium:

   • Total area = area of the rectangle + area of two triangles.
   • Total area = $30 \, \text{m}^2 + 5 \, \text{m}^2 + 5 \, \text{m}^2 = 40 \, \text{m}^2$.

Thus, the area of the trapezium is 40 m².

Follow-up Questions:

1. How would the area change if the height was 6 m instead of 5 m?
2. Can you find the area using the trapezium area formula instead of breaking it into shapes?
3. What if the base of the trapezium was 12 m instead of 10 m—what would the new area be?
4. How would the total area change if one of the triangle’s base was doubled?
5. What is the perimeter of the trapezium with the given dimensions?

Tip: The area of a trapezium can also be calculated directly using the formula $\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$.