To find the remaining grassy area of the park after accounting for the triangular flower bed, we first need to calculate the area of both the rectangular park and the triangular flower bed.
Step 1: Calculate the area of the rectangular park.
The area \(A\) of a rectangle is given by the formula: \[ A = \text{length} \times \text{width} \]
For the park: \[ A_{\text{park}} = 50 , \text{meters} \times 40 , \text{meters} = 2000 , \text{square meters} \]
Step 2: Calculate the area of the triangular flower bed.
The area \(A\) of a triangle is given by the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
For the flower bed: \[ A_{\text{flower bed}} = \frac{1}{2} \times 20 , \text{meters} \times 15 , \text{meters} = \frac{1}{2} \times 300 = 150 , \text{square meters} \]
Step 3: Calculate the remaining grassy area of the park.
Now we subtract the area of the triangular flower bed from the area of the park: \[ \text{Remaining grassy area} = A_{\text{park}} - A_{\text{flower bed}} \] \[ \text{Remaining grassy area} = 2000 , \text{square meters} - 150 , \text{square meters} = 1850 , \text{square meters} \]
Thus, the remaining grassy area of the park is \(\boxed{1850}\) square meters.