Question

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

The length can be found by calculating the distance between two points on the same - y - coordinate. For points (-4,4) and (0,4), using the distance formula for points on a horizontal line \(d=\vert x_2 - x_1\vert\), we have \(l=\vert0-(-4)\vert = 4\). The width can be found by calculating the distance between two points on the same - x - coordinate. For points (0,4) and (0, - 1), using the distance formula for points on a vertical line \(d=\vert y_2 - y_1\vert\), we have \(w=\vert4-(-1)\vert = 5\).

Step2: Calculate the area

The area formula of a rectangle is \(A = l\times w\). Substituting \(l = 4\) and \(w = 5\), we get \(A=4\times5=20\).

Step3: Calculate the perimeter

The perimeter formula of a rectangle is \(P = 2(l + w)\). Substituting \(l = 4\) and \(w = 5\), we have \(P=2(4 + 5)=2\times9 = 18\).

Answer:

Area: 20 square units
Perimeter: 18 units