Question

One container of fertilizer covers 900 square feet. A property has a rectangular backyard that is 30 feet long and 20

feet wide. The front yard is triangular with a base of 24 feet and a height of 12 feet. What percentage of the container
will be used on the property? Round to the nearest percentage.

Answer 1

82.67% of the fertilizer will be used on the property.

Explanation:

Area of Plane Figures

The backyard described in the problem has two parts: One with a rectangular shape of 30 feet by 20 feet. The other with a triangular shape with a base of 24 feet and a height of 12 feet.

The area of a rectangle is calculated by:

`A_r=L*W`

And the area of a triangle is:

`\displaystyle A_t=(B*H)/(2)`

All the backyard will be covered by fertilizer coming from a container with a capacity of 900 square feet.

The total area of the backyard is the sum of the area of the rectangle Ar and the area of the triangle At as follows:

`A_r=30*20=600\ ft^2`

`\displaystyle A_t=(24*12)/(2)=144\ ft^2`

The total area of the backyard is:

`A=600\ ft^2+144\ ft^2=744\ ft^2`

To find the percentage of the container, we calculate:

`\displaystyle (744)/(900)*100\%=82.67\%`

82.67% of the fertilizer will be used on the property.