A triangular lot is 120ft on one side and has a property line of 700ft. Find the area of the lot in acres (figure not drawn to scale)
To find the area of a triangular lot, we need to use the formula for the area of a triangle:
Area = (base * height) / 2
In this case, we have a triangular lot where one side is 120ft long, and we need to find the height of the triangle.
To find the height, we can use the Pythagorean theorem. The property line of the triangle acts as the hypotenuse of a right triangle, and the side of length 120ft is one of the legs. Let's call the height of the triangle "h."
Using the Pythagorean theorem, we have:
h^2 + 120^2 = 700^2
Simplifying the equation:
h^2 = 700^2 - 120^2
h^2 = 490000 - 14400
h^2 = 475600
Taking the square root of both sides:
h = √475600
h ≈ 689.23 ft (rounded to two decimal places)
Now that we have the height, we can calculate the area of the triangle:
Area = (base * height) / 2 = (120 * 689.23) / 2 = 41353.8 ft² (rounded to one decimal place)
Now we can convert the area from square feet to acres. Since 1 acre is equal to 43,560 square feet, we divide the area in square feet by 43,560:
Area in acres = 41353.8 / 43560 ≈ 0.95 acres (rounded to two decimal places)
Therefore, the area of the lot is approximately 0.95 acres.