Trapezoid abcd is graphed in a coordinate plane.

what is the area of the trapezoid?

10 square units
12 square units
20 square units
24 square units

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

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 =

Area of triangle BCD

=

Area of trapezium = 4+8 = 12 square units

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

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step-by-step explanation:

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step-by-step explanation:

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