1. In order to calculate the are which the farmer plans to use for vegetation, you take into account the following formula for the are of a triangle:
where b is the base and h is the height of the triangle. In this case you don't have these parameters, then, you have to calculate them.
To calculate b, the base of the triangle, you consider that a line which crosses the middle of the base of the triangle until the top of the triangle, makes that you have a hypotenuse of 283 yards, just as you can notice in the following image:
Then, you use the trigonoetric relations to find the values of the height of the traingle and its base. You proceed as follow:
For the base you have:
b/2 = 283 cos(80) = 49.14 => b = 98.28
For the height h:
h = 283 sin(80) = 278.7
Once you have the values of b and h, you can calculate the are of one of the traingles:
But the previous one is the are of one triangle. The farmer plan is to use two traingle as it is shown in the picture. Then, the are is 2 x (13,695.34) = 27,390.69 yards²
2. The bag of topsoil costs $12 and covers 36 yards². In order to calculate the cost to cover the total area of vegetation, you first calculate the cost per yard². To calculate this, you divide the cost of 36 yards² between 36 yards², just as follow:
12/36 = 1/3 = 0.33
that is, each yard² costs $0.33. Now, you multiply this factor by the total area found in the previous point, and the result is the total cost of the bags of topsoil needed for the vegetation areas:
costs = 0.33 x 13,695.34 = 4,519.46
Hence, the total cost is of $4,519.46