Question

the diagram shows a garden plot. the area of the garden is square feet. the length of fencing required to completely enclose the garden is feet.

Explanation:

Step1: Identify the shape and relevant dimensions

The garden is a trapezoid. The parallel - sides are $AD = 8$ feet and $BC = 10$ feet, and the height $h$ (vertical distance between parallel sides) is $8$ feet.

Step2: Calculate the area of the trapezoid

The area formula of a trapezoid is $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel sides and $h$ is the height. Substitute $a = 8$, $b = 10$, and $h = 8$ into the formula: $A=\frac{(8 + 10)\times8}{2}=\frac{18\times8}{2}=72$ square feet.

Step3: Calculate the lengths of non - parallel sides

For side $AB$, using the distance formula between two points $A(2,12)$ and $B(14,12)$, the length $AB=14 - 2=12$ feet. For side $CD$, using the distance formula between two points $C(8,4)$ and $D(2,4)$, the length $CD = 8 - 2=6$ feet. For side $BC$, the length is $10$ feet and for side $AD$ the length is $8$ feet.

Step4: Calculate the perimeter (length of fencing)

The perimeter $P$ of the trapezoid is the sum of all its sides. $P=AB + BC+CD + AD=12 + 10+6 + 8=36$ feet.

Answer:

The area of the garden is $72$ square feet. The length of fencing required to completely enclose the garden is $36$ feet.