Question

find the perimeter and area of the rectangle with vertices (4, 3), (-3, 3), (-3, -7), and (4, -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

The length of the horizontal - side can be found by calculating the difference in the x - coordinates of two points on the same horizontal line. For points $(4,3)$ and $(-3,3)$, the length $l=\vert4 - (-3)\vert=\vert4 + 3\vert = 7$. The length of the vertical - side can be found by calculating the difference in the y - coordinates of two points on the same vertical line. For points $(4,3)$ and $(4,-7)$, the length $w=\vert3-(-7)\vert=\vert3 + 7\vert = 10$.

Step2: Calculate the perimeter

The formula for the perimeter of a rectangle is $P = 2(l + w)$. Substitute $l = 7$ and $w = 10$ into the formula: $P=2(7 + 10)=2\times17 = 34$.

Step3: Calculate the area

The formula for the area of a rectangle is $A=l\times w$. Substitute $l = 7$ and $w = 10$ into the formula: $A=7\times10 = 70$.

Answer:

Perimeter: 34 units
Area: 70 square units