Question

finding the area of a trapezoid in the coordinate plane. the height, ce, of the trapezoid is 5 units. what is the area of the trapezoid? ad = units. bc = units. the area of the trapezoid is square units. d(0, 13) e(4, 10) c(1, 6) b(5, 3) a(16, 1). 14.8 62.5 108.8 217.6

Explanation:

Step1: Calculate length of AD

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for points $A(16,1)$ and $D(0,13)$.
$AD=\sqrt{(0 - 16)^2+(13 - 1)^2}=\sqrt{(-16)^2+12^2}=\sqrt{256 + 144}=\sqrt{400}=20$

Step2: Calculate length of BC

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

Step3: Calculate area of trapezoid

Use area formula $A=\frac{(b_1 + b_2)h}{2}$, where $b_1 = AD$, $b_2=BC$, $h = 5$.
$A=\frac{(20 + 5)\times5}{2}=\frac{25\times5}{2}=62.5$

Answer:

$AD = 20$ units
$BC = 5$ units
The area of the trapezoid is $62.5$ square units