Question

similarities between finding the perimeter and area of a polygon with and without the coordinate plane

Answer 1

Answer:

A Polygon is shape with straight sides and must be closed. Polygon sides never touch and are classified according to the number of its sides. So:

• A Triangle is any polygon with exactly 3 sides
• A Quadrilateral is any polygon with exactly 4 sides.
• A Pentagon is any polygon with exactly 5 sides.
• An Hexagon is any polygon with exactly 6 sides.
• A Heptagon is any polygon with exactly 7 sides.
• An Octagon is any polygon with exactly 8 sides.
• A Nonagon is any polygon with exactly 9 sides.
• Decagon is any polygon with exactly 10 sides.

1. WITH THE COORDINATE PLANE:

If you have the coordinate plane, there are several ways to calculate the perimeter and area. If the polygon meaning that every side must have the same length and every angle must have the same measure, you just need the coordinates of two points and by using the distance formula you can calculate the length of that side. Then you must multiply the number of sides by that distance and this is the perimeter, but if the polygon is irregular you must calculate the length of each side of the polygon using the distance formula and then make the sum. To compute the area, you must divide the entire polygon in triangles, rectangles, parallelograms, etc, and then calculating the area of each figure using the formulas known for each type of figure.

2. WITHOUT THE COORDINATE PLANE:

If you don't have the coordinate plane, you need to have the length of each side to calculate the perimeter or each side should be calculated by using trigonometry and other mathematical skills. If the polygon is regular or is a known figure (trapezoid, parallelogram, triangle) you can use the formulas you know to compute the area of that figure. On the other hand, if the polygon is irregular you should divide the polygon in other simple figures and calculate each area and then making the sum.

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In conclusion, for both ways you need to have the length of each side to find the perimeter and can use well known formulas to find the area of the figure.