Question

1. parallelogram klmn k(-1,1) l(4,1) m(2,-2) n(-3,-2)

Explanation:

Step1: Calculate the length of side \(KL\)

Use the distance formula for points with the same \(y -\)coordinate: \(d=\vert x_2 - x_1\vert\). For \(K(-1,1)\) and \(L(4,1)\), \(KL=\vert4-(-1)\vert = 5\).

Step2: Calculate the length of side \(KN\)

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For \(K(-1,1)\) and \(N(-3,-2)\), \(KN=\sqrt{(-3 + 1)^2+(-2 - 1)^2}=\sqrt{(-2)^2+(-3)^2}=\sqrt{4 + 9}=\sqrt{13}\approx3.61\).

Step3: Calculate the perimeter

The perimeter \(P\) of a parallelogram is \(P = 2(a + b)\), where \(a = KL = 5\) and \(b=KN\approx3.61\). So \(P=2(5 + 3.61)=2\times8.61 = 17.22\).

Step4: Calculate the area

The base \(b = KL=5\). The height \(h\) is the vertical distance between \(y = 1\) and \(y=-2\), so \(h=\vert1-(-2)\vert = 3\). The area \(A\) of a parallelogram is \(A=b\times h\), so \(A = 5\times3=15\).

Answer:

Perimeter: \(17.22\); Area: \(15\)