Question

a. 36 meters
b. 40 meters
c. 54 meters
d. 60 meters
e. 68 meters

Explanation:

Step1: Identify the lengths of the sides of the trapezoid

From the graph, for the trapezoid \(ABCD\), \(AD = 11 - 2=9\) (vertical side), \(AB\) is horizontal with \(x\) - coordinates of \(A\) and \(B\) being \(2\) and \(4\) respectively, so \(AB = 4 - 2 = 2\), \(DC\) is horizontal with \(x\) - coordinates of \(D\) and \(C\) being \(2\) and \(16\) respectively, so \(DC=16 - 2 = 14\).

Step2: Use the trapezoid - area formula

The area formula of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the parallel sides and \(h\) is the height. Here, \(a = AB = 2\), \(b = DC = 14\), and \(h = AD = 9\). Then \(A=\frac{(2 + 14)\times9}{2}\).

Step3: Calculate the area

First, calculate the sum of the parallel - sides: \(2+14 = 16\). Then, multiply by the height and divide by 2: \(\frac{16\times9}{2}=72\). But it seems there is a misunderstanding. If we assume we want to find the perimeter of the trapezoid.

• \(AB = 2\), \(AD = 9\), \(DC = 14\).
• For side \(BC\), using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), where \(B(4,11)\) and \(C(16,2)\). \(x_1 = 4,y_1 = 11,x_2 = 16,y_2 = 2\). Then \(BC=\sqrt{(16 - 4)^2+(2 - 11)^2}=\sqrt{12^2+( - 9)^2}=\sqrt{144 + 81}=\sqrt{225}=15\).
• The perimeter \(P=AB + BC+CD + DA=2+15 + 14+9 = 40\).

Answer:

B. 40 meters