Question

Two students calculated the area of a polygon in the coordinate plans using different strategies explain the two methods and which do you prefer and why

Answer 1

Answer:

There are following two methods.

1-By using pre programmed calculator

2-By using formoula

Step-by-step explanation:

1-The first method i suggest for the calculation of area is by using the pre programmed calculator.

Enter the vertex clockwise or anticlockwise into the calculator.

this method is very fast but there is a draw back of this method it is unable to calculate the area of self intersecting polygons. This method is most efficient for the simple polygons and we calculate area very fast.

2-To overcome the draw back of above given method i suggest the method calculate the area by using formoula

First number the vertex in clockwise or anticlckwise direction.

Than use the following formoula to calculate the area of polygon.

Area of polygon= $(x_{1}y_{2}-x_{2}y_{1})+(x_{2}y_{3}-x_{3}y_{2})+............+(x_{n}y_{1}-x_{1}y_{n})/2$

here, if area is negative we take mode of it

$x_{n}$ is the x coorinate of nth vertex.

$y_{n}$ is the Y coorinate of nth vertex.

This method is universal. By using this method we can calculate area of any type of the polygon.