Questions: We now have the sem-perimeter and the area of the quadrilateral. To find the radius (f) of the inscribed circle, we will use the relationship between the area, sem-perimeter, and the radius of the incircle: λ=sr Rearranging the formula to isolate r, r=d / ! Substituting the values of A and s: r=inat/46 Evaluating the expression: r=7.65 (approximately) Therefore, the radius of the circular fountain that can be inscribed in the quadrilateral land plot is approximately 7.06 units.

Solution Steps

To solve the given problem, we need to review the steps provided and check for mathematical correctness. The problem involves finding the radius of an inscribed circle in a quadrilateral using the relationship between the area, semi-perimeter, and the radius of the incircle.

1. Identify the formula for the radius of the incircle: \( r = \frac{A}{s} \), where \( A \) is the area and \( s \) is the semi-perimeter.
2. Substitute the given values into the formula.
3. Evaluate the expression to find the radius.

To find the radius \( r \) of the inscribed circle in a quadrilateral, we use the formula: \[ r = \frac{A}{s} \] where \( A \) is the area and \( s \) is the semi-perimeter.

Given that both the area \( A \) and the semi-perimeter \( s \) are equal to 46, we substitute these values into the formula: \[ r = \frac{46}{46} \]

Calculating the above expression gives: \[ r = 1.0 \]

Final Answer