Question

find the perimeter and area 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) perimeter: units area: square units

Explanation:

Step1: Find the length of the sides

Use the distance formula for horizontal and vertical sides. The length between $(-1,3)$ and $(2,3)$ (a horizontal side) is $|2 - (-1)|=3$. The length between $(2,3)$ and $(2,-7)$ (a vertical side) is $|3-(-7)| = 10$.

Step2: Calculate the perimeter

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l = 10$ and $w = 3$. So $P=2(10 + 3)=2\times13 = 26$.

Step3: Calculate the area

The area $A$ of a rectangle is $A=l\times w$. So $A = 10\times3=30$.

Answer:

Perimeter: 26 units
Area: 30 square units