Question

Trapezoid ABCD is graphed in a coordinate plane.

What is the area of the trapezoid?
5
4
3
В
© 10 shyare units
12 square units
20 square units
24 square units
-5 -3 -2 -1
2
3 4
5
no
3
D
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Answer 1

12

Explanation:

he 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