A triangle lot is 170 ft on one side and has a property line of length of 800 ft. Find the area of the lot in acres
Well, let's see. To find the area of a triangle, we can use the formula: A = (base * height) / 2. In this case, the base of the triangle is 170 ft.
Now, we just need to find the height of the triangle. Since the property line has a length of 800 ft, we can use that as the height.
So the area of the triangle is (170 ft * 800 ft) / 2. That's 136,000 square feet.
To convert square feet to acres, we need to divide by 43,560 (the number of square feet in an acre).
So, the area of the lot is 136,000 square feet / 43,560 = 3.12 acres.
So, the lot is about 3.12 acres in size. It sounds like a pretty "triangular-ific" plot of land to me!
To find the area of the lot in acres, we need to determine the area of the triangle first.
The formula for the area of a triangle is:
Area = (base * height) / 2
Given that one side of the triangle (base) is 170 ft, we still need to find the height. We can use the Pythagorean Theorem to find the height.
The formula for the Pythagorean Theorem is:
c^2 = a^2 + b^2
In our case, the property line is the hypotenuse (c) and the base (a) is 170 ft. We can rearrange the formula like this:
b = sqrt(c^2 - a^2)
Given that the length of the property line (c) is 800 ft, we can determine b:
b = sqrt(800^2 - 170^2)
b ≈ sqrt(640000 - 28900)
b ≈ sqrt(611100)
b ≈ 782.13 ft
Now, we can calculate the area of the triangle, using the formula:
Area = (base * height) / 2
Area = (170 ft * 782.13 ft) / 2
Area ≈ 66593.05 ft^2
To convert the area from square feet to acres, we need to divide it by the conversion factor, which is 43,560 square feet per acre:
Area(acres) = Area(ft^2) / 43560
Area(acres) ≈ 66593.05 ft^2 / 43560
Area(acres) ≈ 1.529 acres
Therefore, the area of the lot is approximately 1.529 acres.
To find the area of the triangle lot, we need to use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, one side of the triangle (the base) is given as 170 ft. However, we need to find the height of the triangle.
To find the height, we will consider the property line of the triangle. The property line is given as 800 ft, but we don't know how it is related to the height.
Since we are dealing with a triangle lot, we can assume that the height is perpendicular to the base. This means that the property line forms a right angle with the given side of the triangle.
Using this information, we can create a right-angled triangle, where the base is 170 ft, the hypotenuse (the property line) is 800 ft, and the height is unknown.
Now, we can use the Pythagorean theorem to find the height. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Applying this to our triangle, we have:
height^2 + 170^2 = 800^2
Simplifying this equation can help us find the value of the height.
Once we have the height, we can substitute it into the formula for the area of a triangle to calculate the area in square feet. Then, if needed, we can convert the area from square feet to acres.
Let's solve the equation to find the height of the triangle and then calculate the area.
Area = 1/2 height*base
Assuming that the above are height and base, 170 * 800 = 136,00 sq. feet
1 acre - 43,560 sq. feet
136,000/43,560 = ?