To find the area of a trapezoid, you can follow some easy steps. A trapezoid is a shape that has two sides that are parallel. We call these sides the bases, which we’ll label as (b_1) and (b_2). There is also a height (h) that goes straight up from one base to the other.

Here’s how to work it out:

1. Draw the Trapezoid: Start by drawing the trapezoid. This will help you see how the parts fit together. Make sure to label the bases and the height.

2. Think About a Rectangle: Remember that the area of a rectangle is found by multiplying its length and width. In this case, you can imagine a rectangle that is as tall as the height of the trapezoid and as wide as the longer base.

3. Cut It Into Two Triangles: Now, draw a line connecting the ends of the non-parallel sides (the sides that are not the bases). This will show you that the trapezoid can be split into a rectangle in the middle and two triangles on the sides.

4. Find Each Area: To find the area of the rectangle, use the formula (A_{rectangle} = (b_1 + b_2) \cdot h). The triangles will have bases that show the difference between the lengths of the two bases. When you add the areas of the triangles, you will find the total area of the trapezoid.

5. Combine the Areas: Finally, you can write the area of the trapezoid like this: $A_{trapezoid} = \frac{1}{2}(b_1 + b_2) \cdot h$

This formula takes the two bases, adds them together, and averages them. It gives you the area of the trapezoid, which is useful when learning about geometry in Grade 9.