Question

#3
polygon abcd has
vertices a(-4, -1),
b(-4, 5), c(2, 5),
and d(2, -1). draw
the polygon. what
is the perimeter of
polygon abcd?

Explanation:

Step1: Calculate the length of AB

Since \(A(-4,-1)\) and \(B(-4,5)\), using the distance formula for points with the same \(x\)-coordinate \(d=\vert y_2 - y_1\vert\).
\(AB=\vert5-(-1)\vert=\vert5 + 1\vert = 6\)

Step2: Calculate the length of BC

Since \(B(-4,5)\) and \(C(2,5)\), using the distance formula for points with the same \(y\)-coordinate \(d=\vert x_2 - x_1\vert\).
\(BC=\vert2-(-4)\vert=\vert2 + 4\vert=6\)

Step3: Calculate the length of CD

Since \(C(2,5)\) and \(D(2,-1)\), using the distance formula for points with the same \(x\)-coordinate \(d=\vert y_2 - y_1\vert\).
\(CD=\vert-1 - 5\vert=\vert-6\vert = 6\)

Step4: Calculate the length of DA

Since \(D(2,-1)\) and \(A(-4,-1)\), using the distance formula for points with the same \(y\)-coordinate \(d=\vert x_2 - x_1\vert\).
\(DA=\vert-4 - 2\vert=\vert-6\vert=6\)

Step5: Calculate the perimeter

The perimeter \(P\) of a polygon is the sum of the lengths of its sides. For quadrilateral \(ABCD\), \(P=AB + BC+CD + DA\).
\(P=6 + 6+6 + 6=24\)

Answer:

1. 24 units