Question

this question has two parts. first, answer part a. then, answer part b. part a identify the figure with the vertices q(-3,2), r(1,2), s(1,-4), and t(-3,-4). quadrilateral part b find the perimeter and area of the figure. perimeter: units area: units² need help with this question? get a hint

Explanation:

Step1: Calculate side - lengths

For side QR with $Q(-3,2)$ and $R(1,2)$:
Using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, since $y_1 = y_2 = 2$, $QR=\vert1-(-3)\vert=4$.
For side RS with $R(1,2)$ and $S(1,-4)$:
Since $x_1 = x_2 = 1$, $RS=\vert2-(-4)\vert = 6$.
For side ST with $S(1,-4)$ and $T(-3,-4)$:
Since $y_1 = y_2=-4$, $ST=\vert1 - (-3)\vert=4$.
For side TQ with $T(-3,-4)$ and $Q(-3,2)$:
Since $x_1 = x_2=-3$, $TQ=\vert2-(-4)\vert = 6$.

Step2: Calculate the perimeter

The perimeter $P$ of a quadrilateral is the sum of its side - lengths.
$P=QR + RS+ST + TQ=4 + 6+4 + 6=20$.

Step3: Calculate the area

Since the figure is a rectangle (opposite sides are equal and adjacent sides are perpendicular), the area $A$ of a rectangle is given by $A = length\times width$.
Here, length $l = 6$ and width $w = 4$, so $A=4\times6 = 24$.

Answer:

perimeter: 20 units
area: 24 units²