Question

the length, ce, of the trapezoid is 5 units. what is the area of the trapezoid? ad = \boxed{} units. bc = \boxed{} units. the area of the trapezoid is \boxed{} square units.

Explanation:

Step1: Identify length of AD

Use distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
For $A(16,1)$ and $D(1,12)$:
$$AD=\sqrt{(16-1)^2+(1-12)^2}=\sqrt{15^2+(-11)^2}=\sqrt{225+121}=\sqrt{346}\approx18.60$$

Step2: Identify length of BC

Use distance formula for $B(5,3)$ and $C(1,6)$:
$$BC=\sqrt{(5-1)^2+(3-6)^2}=\sqrt{4^2+(-3)^2}=\sqrt{16+9}=\sqrt{25}=5$$

Step3: Calculate trapezoid area

Use area formula: $A=\frac{1}{2}(b_1+b_2)h$
Here $b_1=AD\approx18.60$, $b_2=BC=5$, $h=5$
$$A=\frac{1}{2}(18.60+5)\times5=\frac{1}{2}(23.60)\times5=11.8\times5=59$$

Answer:

$AD \approx 18.60$ units
$BC = 5$ units
The area of the trapezoid is $59$ square units