To calculate the area of the figure, we will break it into smaller sections. The figure can be decomposed into the following:

1. A large rectangle or parallelogram section in the middle.
2. Two right triangles, one on each side.

Step 1: Break the shape into parts

• Central parallelogram:

  • Its base is $10 \, \text{yd} + 10 \, \text{yd} = 20 \, \text{yd}$.
  • Its height is $5 \, \text{yd}$.

• Two right triangles:

  • Each triangle has a base of $3 \, \text{yd}$ and a height of $4 \, \text{yd}$.

Step 2: Calculate the area of each section

1. Central parallelogram: $\text{Area} = \text{base} \times \text{height} = 20 \, \text{yd} \times 5 \, \text{yd} = 100 \, \text{yd}^2$

2. Each right triangle: $\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3 \, \text{yd} \times 4 \, \text{yd} = 6 \, \text{yd}^2$ Since there are two triangles: $\text{Total area of triangles} = 2 \times 6 \, \text{yd}^2 = 12 \, \text{yd}^2$

Step 3: Add the areas

$\text{Total area} = \text{Area of parallelogram} + \text{Total area of triangles}$ $\text{Total area} = 100 \, \text{yd}^2 + 12 \, \text{yd}^2 = 112 \, \text{yd}^2$

Final Answer:

The area of the figure is 112 square yards.

Would you like a detailed breakdown of this explanation or further clarifications?

Related Questions:

1. How would the calculation change if the triangles' dimensions were different?
2. What is the perimeter of this figure?
3. How can this method of breaking shapes into parts be applied to other composite figures?
4. What is the formula for the area of a parallelogram, and why does it work?
5. What other ways could this shape be decomposed?

Tip:

When calculating areas of composite shapes, always start by identifying simple geometric sections such as rectangles, triangles, and circles.