To find the area of the trapezoid shown in the image, we can use the formula for the area of a trapezoid:

$\text{Area} = \frac{1}{2} \times (a + b) \times h$

where:

• $a$ and $b$ are the lengths of the two parallel sides (the bases),
• $h$ is the height (the perpendicular distance between the bases).

From the image, we have:

• One base $a = 9 \text{ cm}$,
• The other base $b = 6 \text{ cm}$,
• The height $h = 3 \text{ cm}$.

Plugging these values into the formula:

$\text{Area} = \frac{1}{2} \times (9 \text{ cm} + 6 \text{ cm}) \times 3 \text{ cm}$ $\text{Area} = \frac{1}{2} \times 15 \text{ cm} \times 3 \text{ cm}$ $\text{Area} = \frac{1}{2} \times 45 \text{ cm}^2$ $\text{Area} = 22.5 \text{ cm}^2$

Therefore, the area of the trapezoid is $22.5 \text{ cm}^2$.

Do you want any details or have any questions?

Here are some related questions to expand your understanding:

1. How would the area change if the height was 4 cm instead of 3 cm?
2. What is the formula for the perimeter of a trapezoid?
3. How do you derive the area formula for a trapezoid?
4. What are the properties of a trapezoid?
5. How can you find the height of a trapezoid if it's not given?
6. How would the area change if one of the bases was doubled?
7. Can you calculate the area if only the lengths of the non-parallel sides and the height are given?
8. What are some real-life applications of finding the area of trapezoids?

Tip: Always double-check your measurements and units when calculating the area to ensure accuracy.