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
