Question

What is the area of the composite figure whose vertices have the following coordinates? (−2, −2) , (4, −2) , (5, 1) , (2, 3) , (−1, 1) Enter your answer in the box. units²

Answer 1

24 units is the correct answer!

Answer 2

24 square units

Explanation:

Try this method. First write the coordinates of each point on a new line. Repeat the first point at the bottom after the dashed line.

-2 -2

4 -2

5 1

2 3

-1 1

----------

-2 -2

Now multiply each x-coordinate from the left column by the y-coordinate below it in the right column and write the answer to the right. I did it below in bold.

-2 -2

4 -2 4

5 1 4

2 3 15

-1 1 2

----------

-2 -2 2

Now multiply each y-coordinate from the right column by the x-coordinate below it in the left column and write the answer to the left. I did it below in bold.

-2 -2

-8 4 -2 4

-10 5 1 4

2 2 3 15

-3 -1 1 2

----------

-2 -2 -2 2

Add the numbers in the left bold column and add the number in the right bold column.

-2 -2

-8 4 -2 4

-10 5 1 4

2 2 3 15

-3 -1 1 2

----------

-2 -2 -2 2

--------------------------------

-21 27

The area of the polygon is the absolute value of half of the right sum minus the left sum.

A = | 1/2 (right sum - left sum) |

A = | 1/2 (27 - (-21) |

A = | 1/2(48) |

A = |24|

A = 24

Area = 24 square units