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

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

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:

• $b_1 = 5$ feet (top base)
• $b_2 = 10$ feet (bottom base)
• $h = 4$ feet

Plugging these values into the formula, we get:

$\text{Area} = \frac{1}{2} \times (5 + 10) \times 4$

$\text{Area} = \frac{1}{2} \times 15 \times 4$

$\text{Area} = \frac{1}{2} \times 60$

$\text{Area} = 30 \, \text{square feet}$

So, the area of the trapezoid is 30 square feet.

Would you like more details on the solution or have any questions? Here are some related questions you might find interesting:

1. How do you derive the formula for the area of a trapezoid?
2. What are the properties of a trapezoid?
3. How can the area of a trapezoid be applied in real-life situations?
4. What is the formula for the perimeter of a trapezoid?
5. How would the area change if the height were increased to 6 feet?
6. How would you calculate the area of a trapezoid if the non-parallel sides were given instead of the height?
7. Can the area formula for a trapezoid be used for any other quadrilaterals?
8. What are some examples of trapezoids in architecture and engineering?

Tip: When solving problems involving geometric shapes, always make sure to double-check the given measurements and ensure they are in the correct units before performing calculations.