Final answer:
To fence and seed the farmer's land, the total fenced perimeter is 770 yards, and the total area for seeding is 229,500 square feet. The total cost for fencing is $20,790 and for seeding is $459,000, adding up to a total cost of $479,790.
Step-by-step explanation:
To calculate the total cost to fence and seed the square and isosceles triangular sections of land owned by the farmer, we first need to determine the perimeter of the land to be fenced and the area that needs to be seeded.
Square Piece of Land
The side length of the square is 450 feet, so its perimeter is:
Perimeter (square) = 4 × side = 4 × 450 feet = 1800 feet
Area (square) = side × side = 450 feet × 450 feet = 202500 square feet
Triangular Piece of Land
For the triangular piece of land, we have two sides with the length of 255 feet. The base of the triangle is shared with one side of the square, so it's not included again in fencing calculations. However, we'll need the area to calculate the seeding costs.
Perimeter (triangle sides only) = 2 × 255 feet = 510 feet
Area (triangle) = 0.5 × base × height = 0.5 × 450 feet × 120 feet = 27000 square feet
Total Costs
The total perimeter needing fencing is the sum of the square's perimeter and the two sides of the triangle:
Total perimeter = 1800 feet + 510 feet = 2310 feet
Total area = 202500 square feet + 27000 square feet = 229500 square feet
Convert perimeter to yards (1 yard = 3 feet):
Total perimeter in yards = 2310 feet / 3 = 770 yards
Now, calculate the total costs:
Fencing cost = 770 yards × $27/yard = $20790
Seeding cost = 229500 square feet × $2/square foot = $459000
Total cost = Fencing cost + Seeding cost = $20790 + $459000 = $479790