To solve this problem, let’s analyze the provided diagram and the information given. Here’s a step-by-step outline to calculate the total area of the grass.

Problem Analysis

1. Shape and Dimensions: The garden has a trapezoidal shape, divided into sections labeled as "grass" and "path."
2. Measurements: All lengths in feet:
   • The trapezoid has two parallel sides:
     • Bottom: $25$ feet
     • Top: $12$ feet
   • Height of the trapezoid: $15$ feet.
3. Paths and Grass Areas: The garden is split by two diagonal paths, creating three main regions of grass.

Approach to Solution

1. Calculate Total Area of the Trapezoid: The total area of a trapezoid is given by: $\text{Area} = \frac{1}{2} \times (a + b) \times h$ where $a$ and $b$ are the lengths of the parallel sides, and $h$ is the height.

2. Determine the Area of the Paths: After calculating the total area, subtract the area covered by the paths to find the grass area.

Step-by-Step Calculation

1. Calculate the Total Area of the Garden (Trapezoid)

Using the trapezoid area formula:

• $a = 25$ feet
• $b = 12$ feet
• $h = 15$ feet

$\text{Total Area} = \frac{1}{2} \times (25 + 12) \times 15 = \frac{1}{2} \times 37 \times 15 = 277.5 \text{ square feet}$

2. Estimate the Area of the Paths

The paths appear to form two triangles. We would need specific measurements or a clear strategy to divide the path area precisely. Assuming approximate values or specific ratios would be speculative without further information.

3. Calculate Total Area of Grass

With the area of the paths subtracted, we would obtain the grass area.

Could you clarify or provide additional path dimensions for more accurate path area estimation?

Follow-Up Questions:

1. Would you like a detailed calculation assuming specific areas for the paths?
2. Do you need help with calculating areas of the triangular path sections?
3. Would additional diagrams assist in visualizing calculations for complex shapes?
4. Should we explore methods to estimate areas of irregular sections?
5. Are there other areas in the diagram that need further clarification?

Tip: When dealing with composite shapes, breaking down areas into familiar geometric forms helps simplify calculations.