You are making a garden in a triangular lot, and needed a top soil of mixed humus and fertilized. what is the area of the lot needed to cover by soil if the edge of the lot measures 10ft.,8ft. and 6ft.,?
This is a rt. triangle:
A = 0.5b*h = 0.5*6*8 = 24 Ft^2.
To find the area of a triangular lot, you can use Heron's formula. Heron's formula states that the area of a triangle with side lengths a, b, and c is given by:
Area = sqrt(s * (s - a) * (s - b) * (s - c))
where s is the semi-perimeter of the triangle, which is calculated as:
s = (a + b + c) / 2
In your case, the side lengths of the triangular lot are given as 10ft, 8ft, and 6ft. So, we can substitute these values into the formulas.
Calculating the semi-perimeter:
s = (10ft + 8ft + 6ft) / 2
s = 24ft / 2
s = 12ft
Calculating the area:
Area = sqrt(12ft * (12ft - 10ft) * (12ft - 8ft) * (12ft - 6ft))
Area = sqrt(12ft * 2ft * 4ft * 6ft)
Area = sqrt(576ft^2)
Area = 24ft^2
Therefore, the area of the lot that would be needed to cover by soil is 24 square feet.