Final answer:
To calculate the perimeter and area of polygons on a coordinate plane, plot the vertices, use the distance formula to find the lengths between points, and then add the lengths for the perimeter. To find the area, you may need to break irregular shapes into regular sections. Conversion from polar to Cartesian coordinates may be necessary for calculating distances.
Step-by-step explanation:
Using Coordinates to Find Perimeter and Area
Calculating the perimeter and area of polygons using coordinates involves a series of steps. First, you need to plot all the vertices of the polygon on the coordinate plane. Then, you can calculate the distances between adjacent vertices using the distance formula for the Cartesian coordinates. For diagonal sides, the formula will be the square root of the sum of the squares of the differences in x and y coordinates of the two points. After determining all sides' lengths, add them to get the perimeter. For the area, if it's a regular shape, apply standard formulae like length × width for rectangles. For irregular shapes, you might need to divide the polygon into smaller sections such as triangles or rectangles, find the area of each, and sum them.
When dealing with polar coordinates, you need to convert them to Cartesian coordinates if the sides are not radii of circles or arcs. To convert polar coordinates (r, θ) to Cartesian coordinates (x, y), use x = r × cos(θ) and y = r × sin(θ). If you are comparing the area of shapes, use proportions to understand the relationship between them.
Remember, the units are essential; if you're working with meters, the perimeter will be in meters, and the area will be in square meters. Lastly, for volumes with cubes, you will use the cube of the side length, which would be in cubic meters.