Question

unit 2 review - monday, september 22
find the perimeter and area of abcd

Explanation:

Step1: Find length of AB

AB is a horizontal line - segment. Co - ordinates of A(-3,4) and B(1,4). Using the distance formula for horizontal line \(d = |x_2 - x_1|\), \(AB=|1-(-3)| = 4\).

Step2: Find length of BC

Co - ordinates of B(1,4) and C(5,0). Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), \(BC=\sqrt{(5 - 1)^2+(0 - 4)^2}=\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2}\).

Step3: Find length of CD

Co - ordinates of C(5,0) and D(-4,0). Using the distance formula for horizontal line \(d = |x_2 - x_1|\), \(CD=|5-(-4)| = 9\).

Step4: Find length of DA

Co - ordinates of D(-4,0) and A(-3,4). Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), \(DA=\sqrt{(-3+4)^2+(4 - 0)^2}=\sqrt{1 + 16}=\sqrt{17}\).

Step5: Calculate perimeter P

\(P=AB + BC+CD + DA=4 + 4\sqrt{2}+9+\sqrt{17}=13 + 4\sqrt{2}+\sqrt{17}\approx13+4\times1.414 + 4.123=13 + 5.656+4.123 = 22.779\).

Step6: Calculate area A

The trapezoid has bases \(b_1 = 4\) and \(b_2=9\) and height \(h = 4\). Using the area formula for a trapezoid \(A=\frac{(b_1 + b_2)h}{2}\), \(A=\frac{(4 + 9)\times4}{2}=\frac{13\times4}{2}=26\).

Answer:

Perimeter \(P = 13 + 4\sqrt{2}+\sqrt{17}\approx22.78\), Area \(A = 26\)