answer to to question to the one i just asked

Question

Identify the area of the polygon that has vertices A (0, 3), B (5, 5), C (7, 3), and D (3, 1).

Answer 1

It really, really helps to draw a picture (or plot the polygon)!    [most people can't "see" the picture quickly from points in Cartesian Coordinate form.

 

 

       |  [note:  Not to scale]

       |

       |

       |                                  B

       |

       A                                                C

       |

       |                    D

- - - - - - | - - | - - | - - | - - | - - | - - | - - |

 

 

Now, segment AC is horizontal (because the y-values are identical), so cut the polygon into two triangles with width&height of 7&2 and 7&2.

 

Area of polygon = area of top triangle  + area of bottom triangle

Area of polygon = (1/2)(7)(2)             + (1/2)(7)(2)

Area of  polygon = 7+7

Area of polygon = 14 square units