To find the area of the composite shape shown in the image, which consists of two triangles, we need to break it down into its individual triangular components and find the area of each. Let's first identify the two triangles and their dimensions:

1. Left Triangle:

   • Base: 6 yards
   • Height: 4 yards

2. Right Triangle:

   • Base: 14 yards - 6 yards = 8 yards (since the total base of the larger triangle is 14 yards)
   • Height: 4 yards

We will use the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Step 1: Calculate the area of the left triangle

$\text{Area}_{\text{left}} = \frac{1}{2} \times 6 \times 4$ $\text{Area}_{\text{left}} = \frac{1}{2} \times 24$ $\text{Area}_{\text{left}} = 12 \, \text{square yards}$

Step 2: Calculate the area of the right triangle

$\text{Area}_{\text{right}} = \frac{1}{2} \times 8 \times 4$ $\text{Area}_{\text{right}} = \frac{1}{2} \times 32$ $\text{Area}_{\text{right}} = 16 \, \text{square yards}$

Step 3: Add the areas of both triangles to get the total area

$\text{Total Area} = \text{Area}_{\text{left}} + \text{Area}_{\text{right}}$ $\text{Total Area} = 12 + 16$ $\text{Total Area} = 28 \, \text{square yards}$

So, the total area of the composite shape is 28 square yards.

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 find the area of a triangle when only the sides are known?
2. What are the properties of a right triangle?
3. How can the area of a triangle be applied in real-life situations?
4. How would you calculate the area of a triangle if the height were not given?
5. Can the formula for the area of a triangle be used for any other polygons?
6. What are some examples of composite shapes in architecture and engineering?
7. How do you find the area of a shape with more than two triangles?
8. How would the total area change if the height of the triangles were increased to 6 yards?

Tip: When working with composite shapes, always break them down into simpler components (such as triangles or rectangles) to make calculations easier.