Question

A farmer has a field in the shape of a trapezoid, formed by three congruent isosceles triangles, as shown below. He wants to plant vegetation in the green shaded area and pour concrete in the remaining area. What area of the field does the farmer plan to use for vegetation planting? Round your answer to the nearest tenth of a square yard. If a bag of top soil costs $12 and covers 36 square yards, how much will it cost the farmer to cover the vegetation part of his field with the top soil?

Answer 1

Answer:

1) 52559.6 sq.yards

2) $17186.5

Step-by-step explanation:

1) Since, all three are congruent isosceles triangles.

=>  EC=185  yards, BE=BC=283 yards.

$\angle C=80^{\circ}$

Now,

Area of field farmer uses for vegetation planting  = Area of two congruent triangle = 2*Area of triangle BEC

2*Area of $\triangle BEC$

$=2*\frac{1}{2}*BC*EC*sin(80^{\circ})\\ \\=2*\frac{1}{2}*283*185*sin(80^{\circ})\\ \\=51559.6\:sq.yards$

2) Bag of top soil costs $12 per 36 sq. yards.

=> 1 sq. yard will cost $12/36=$1/3

=>51559.6 sq. yards will cost =1/3*51559.6=$17186.5.

Hence,

Finally ,

Area of field used for vegetative planting will be 51559.6 sq yads and cost to cover vegetative part of his field with the top soil will be $17186.5.