Question

find the area and perimeter of the rectangle with vertices $(-1,3),(2,3),(2,-7)$, and $(-1,-7)$. note that you can draw in the scratch area below, but it is not part of the answer.
scratch area (not part of answer)
area: $square$ square units
perimeter: $square$ units

Explanation:

Step1: Calculate the length and width

The length \( l \) of the rectangle is the difference in the \( x -\)coordinates of two adjacent vertices: \( l=\vert2 - (- 1)\vert=3 \) units.
The width \( w \) of the rectangle is the difference in the \( y -\)coordinates of two adjacent vertices: \( w=\vert3-(-7)\vert = 10 \) units.

Step2: Calculate the area

The formula for the area \( A \) of a rectangle is \( A=l\times w \).
Substitute \( l = 3 \) and \( w = 10 \) into the formula: \( A=3\times10=30 \) square units.

Step3: Calculate the perimeter

The formula for the perimeter \( P \) of a rectangle is \( P = 2(l + w) \).
Substitute \( l = 3 \) and \( w = 10 \) into the formula: \( P=2(3 + 10)=2\times13 = 26 \) units.

Answer:

Area: \( 30 \) square units
Perimeter: \( 26 \) units