Question

Figure ABCD has vertices A(−3, 2), B(2, 2), C(2, −4), and D(−3, −2). What is the area of Figure ABCD? 5 square units 20 square units 25 square units 40 square units

Answer 1

Answer:

The area of Figure ABCD is 25 square units

Step-by-step explanation:

we have

A(−3, 2), B(2, 2), C(2, −4), and D(−3, −2)

step 1

Plot the figure

using a graphing tool

The figure is a trapezoid

see the attached figure

step 2

Find the area of the trapezoid

The area of the trapezoid is equal to

$A=\frac{1}{2}[AD+BC]AB$

we have

$AD=2-(-2)=4\ units$ ---> difference in the y-coordinates

$BC=2-(-4)=6\ units$ ---> difference in the y-coordinates

$AB=2-(-3)=5\ units$ ---> difference in the x-coordinates

substitute

$A=\frac{1}{2}[4+6]5$

$A=25\ units^{2}$