Question

Trapezoid ABCD is graphed in a coordinate plane.

Answer 1

Answer: Using the coordinates of its vertices, the area of the trapezoid is

12 square units (Second option)

Solution:

The coordinates of the vertices of the trapezoid ABCD are:

A=(-5,-2)=(xa,ya)→xa=-5, ya=-2

B=(-1,2)=(xb,yb)→xb=-1, yb=2

C=(0,-1)=(xc,yc)→xc=0, yc=-1

D=(-2,-3)=(xd,yd)→xd=-2, yd=-3

yi x(i+1)        xi     yi     xi y(i+1)

                  -5    -2

(-2)(-1)=2     -1      2     (-5)(2)=-10

(2)(0)=0       0     -1     (-1)(-1)=1

(-1)(-2)=2    -2    -3     (0)(-3)=0

(-3)(-5)=15   -5    -2     (-2)(-2)=4

S1=-10+1+0+4→S1=-5

S2=2+0+2+15→S2=19

Area: A=(1/2) Absolute value (S1-S2)

A=(1/2) Absolute value (-5-19)

A=(1/2) Absolute value (-24)

A=(1/2) (24)

A=24/2

A=12

The area of the trapezoid is 12 square units

Answer 2

Answer:

Option B 12 square units

Step-by-step explanation:

Given is a trapezoid drawn on a graph.

Vertices of the trapezium are (-1,2) (0,-1) (-2,-3) and (-5,-2)

The area of trapezium can be found as area of two triangles

Area of triangle ABD =

$\frac{1}{2} \left[\begin{array}{ccc}-1&2&1\\0&-1&1\\-2&-3&1\end{array}\right] \\\\=\frac{1}{2} [-1(-1+3)-2(2+1)]=4 square units$

Area of triangle BCD

=$\frac{1}{2} \left[\begin{array}{ccc}-5&-2&1\\0&-1&1\\-2&-3&1\end{array}\right] \\\\=\frac{1}{2} [-5(-1+3)-2(-2+1)]=8 square units$

Area of trapezium = 4+8 = 12 square units

(NOte: Area cannot be negative hence absolute value is taken)