Question

What is the area of parallelogram ABCD? ____ square units

Answer 1

Answer:

13

Step-by-step explanation:

Here's a method of finding the area of any polygon knowing its vertices. I'm using this parallelogram as an example.

Make a table like this (each vertex with its x- and y-coordinates):

Pt    x       y

A     3      6

B     6      5

C     5      1

D     2      2

A     3      6

Now multiply each x-coordinate by the y-coordinate on the line below and write it on the right side. Bold type shows the first multiplication.

       x       y

A     3      6

B     6      5      15

C     5      1        6

D     2      2      10

A     3      6      12

Now multiply each y-coordinate by the x-coordinate on the line below and subtract from each produce you already have. Do each subtraction. Bold type shows the first multiplication.

       x       y

A     3     6

B     6      5      15 - 36 = -21

C     5      1        6 - 25 = -19

D     2      2      10 - 2 =     8

A     3      6      12 - 6 =     6

Add all the differences.

       x       y

A     3      6

B     6      5      15 - 36 = -21

C     5      1        6 - 25 = -19

D     2      2      10 - 2 =     8

A     3      6      12 - 6 =     6

                                   +____

                                       -26

The area of the polygon is the absolute value of half of the sum of the differences.

area = |-26/2| = |-13| = 13