Question

find the area and perimeter of the rectangle with vertices (4, 0), (4, - 3), (-1, - 3), and (-1, 0). 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 units perimeter: units

Explanation:

Step1: Find the length of the sides

The length of the horizontal - side can be found by calculating the distance between two points with the same y - coordinate. For points $(4,0)$ and $(-1,0)$, using the distance formula for points on a horizontal line $d = |x_2 - x_1|$, we have $d_1=|4-(-1)| = 5$.
The length of the vertical - side can be found by calculating the distance between two points with the same x - coordinate. For points $(4,0)$ and $(4, - 3)$, using the distance formula for points on a vertical line $d = |y_2 - y_1|$, we have $d_2=|0 - (-3)|=3$.

Step2: Calculate the area

The area formula of a rectangle is $A = l\times w$. Here, $l = 5$ and $w = 3$, so $A=5\times3 = 15$ square units.

Step3: Calculate the perimeter

The perimeter formula of a rectangle is $P=2(l + w)$. Substituting $l = 5$ and $w = 3$ into the formula, we get $P = 2(5 + 3)=16$ units.

Answer:

Area: 15 square units
Perimeter: 16 units