Question

type the correct answer in each box. the diagram shows a garden plot. the area of the garden is blank square feet. the length of fencing required to completely enclose the garden is blank feet.

Explanation:

Step1: Identify the shape and find area

The garden is a trapezoid. The formula for the area 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. From the graph, the parallel sides are $a = 4$ and $b=12$, and the height $h = 10$.
$A=\frac{(4 + 12)\times10}{2}$
$A=\frac{16\times10}{2}=80$ square feet.

Step2: Find the lengths of non - parallel sides

For side $AB$, since it is a horizontal line, the length of $AB$ can be found by the difference in $x$ - coordinates of $A$ and $B$. Let $A=(2,12)$ and $B=(14,12)$, then $AB=\vert14 - 2\vert=12$ feet.
For side $BC$, using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $B=(14,12)$ and $C=(10,4)$.
$d_{BC}=\sqrt{(14 - 10)^2+(12 - 4)^2}=\sqrt{4^2+8^2}=\sqrt{16 + 64}=\sqrt{80}=4\sqrt{5}\approx8.94$ feet.
For side $CD$, since it is a horizontal line, let $C=(10,4)$ and $D=(2,4)$, then $CD=\vert10 - 2\vert = 8$ feet.
For side $DA$, since it is a vertical line, let $D=(2,4)$ and $A=(2,12)$, then $DA=\vert12 - 4\vert=8$ feet.
The perimeter $P=AB + BC+CD + DA=12+4\sqrt{5}+8 + 8=28 + 4\sqrt{5}\approx28+8.94 = 36.94$ feet.

Answer:

Area: 80
Perimeter: $28 + 4\sqrt{5}\approx36.94$