To find the area of a trapezoid, we use the formula:

$\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h$

where:

• $b_1$ and $b_2$ are the lengths of the two parallel sides (the bases),
• $h$ is the height (the perpendicular distance between the bases).

From the image:

• $b_1 = 10 \, \text{in}$
• $b_2 = 6 \, \text{in}$
• $h = 5 \, \text{in}$

Now, plug in these values:

$\text{Area} = \frac{1}{2} \times (10 + 6) \times 5$

$\text{Area} = \frac{1}{2} \times 16 \times 5$

$\text{Area} = 8 \times 5 = 40 \, \text{in}^2$

The area of the trapezoid is 40 square inches.

Would you like further details, or have any other questions?

Here are 5 related questions for further exploration:

1. What is the perimeter of the trapezoid?
2. How would you find the area if the height wasn't given directly?
3. What happens to the area if both bases are doubled?
4. How do you find the length of the non-parallel sides of a trapezoid if you know the area?
5. What are some real-world applications of calculating the area of a trapezoid?

Tip: When working with trapezoids, always double-check which sides are the parallel bases and ensure the height is perpendicular to them.