The problem states that an artist joins two triangular pieces of metal together to form a parallelogram, and each grid square represents 1 square foot.

Let's solve the problem step-by-step:

1. Identify the Area of Each Triangle:

   • From the image, each triangle is drawn on a 5x3 grid.
   • Since each grid square represents 1 square foot, we can calculate the area of each triangle.
   • The formula for the area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.
   • Here, the base is 5 feet, and the height is 3 feet.
   • Therefore, the area of one triangle is $\frac{1}{2} \times 5 \times 3 = 7.5$ square feet.

2. Calculate the Area of the Parallelogram:

   • Since the parallelogram is made by joining two identical triangles, its total area is twice the area of one triangle.
   • So, the area of the parallelogram is $2 \times 7.5 = 15$ square feet.

Thus, the area of the parallelogram is 15 square feet.

Would you like further details or explanations on this problem? Here are some related questions you might find interesting:

1. How do you calculate the perimeter of a parallelogram given its base and height?
2. How can you verify the shape formed is a parallelogram using its properties?
3. What are the different ways to calculate the area of a parallelogram?
4. How do the properties of parallelograms apply to other quadrilaterals like rectangles or rhombuses?
5. How does changing the base or height of a triangle affect the area of the resulting parallelogram?

Tip: Always check if the shapes are identical when combining them to form new geometric figures, as this affects calculations like area and perimeter.