To find the total area of the pasture, we need to find the areas of both the semi-circular grassy area and the triangular riding area, and then add them together.
First, let's find the area of the semi-circular grassy area:
The diameter of the grassy area is equal to the height of the riding area, which is 75 feet. The radius of the grassy area is half of the diameter, so it is 75 feet divided by 2, which is 37.5 feet.
The formula to find the area of a semi-circle is A = (Ï€ * r^2) / 2, where A is the area and r is the radius.
Substituting the values, we get A = (Ï€ * (37.5 feet)^2) / 2.
Simplifying the equation, we get A = π * (37.5 feet)^2 / 2.
Using the approximation for π as 3.14, we can calculate the area:
A ≈ 3.14 * (37.5 feet)^2 / 2.
A ≈ 3.14 * 1406.25 feet^2 / 2.
A ≈ 4397.0625 feet^2 / 2.
A ≈ 2198.53125 feet^2.
Next, let's find the area of the triangular riding area:
The base of the riding area is given as 50 feet, and the height is also given as 75 feet.
The formula to find the area of a triangle is A = (base * height) / 2.
Substituting the values, we get A = (50 feet * 75 feet) / 2.
Simplifying the equation, we get A = 3750 feet^2 / 2.
A = 1875 feet^2.
Finally, let's find the total area of the pasture by adding the areas of the grassy area and the riding area:
Total Area = Area of grassy area + Area of riding area.
Total Area = 2198.53125 feet^2 + 1875 feet^2.
Total Area ≈ 4073.53125 feet^2.
Rounding to the nearest tenth, the total area of the pasture is approximately 4073.5 square feet.