To calculate the area of the park shown in the image, the shape is split into two parts: a rectangle and a triangle.

Step 1: Area of the rectangle

The rectangle has dimensions:

• Length = 40 yards
• Width = 30 yards

The area of the rectangle is: $\text{Area}_{\text{rectangle}} = \text{Length} \times \text{Width} = 40 \times 30 = 1200 \, \text{square yards}.$

Step 2: Area of the triangle

The triangle has:

• Base = 40 yards (same as the rectangle's length)
• Height = 20 yards (as labeled in the image)

The area of the triangle is: $\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 40 \times 20 = 400 \, \text{square yards}.$

Step 3: Total area

The total area of the park is the sum of the rectangle and triangle areas: $\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle}} = 1200 + 400 = 1600 \, \text{square yards}.$

Final Answer:

The area of the park is 1600 square yards.

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Would you like further clarification or a breakdown of any step?

Related Questions:

1. How do you calculate the perimeter of this park?
2. How would the total area change if the triangle's height increased by 10 yards?
3. How can you find the area of irregular shapes without dividing them into simpler parts?
4. What are other geometric formulas for calculating areas of shapes?
5. What is the significance of right angles in area calculations?

Tip:

When solving for the area of irregular shapes, always aim to divide the shape into well-known geometric figures like triangles and rectangles!