Draw and classify the polygon with the given vertices. Find the perimeter and area of the polygo

Draw and classify the polygon with the given vertices. Find...

Key Concepts

Polygon Classification

Polygon classification involves determining the specific type of polygon based on its properties such as side lengths, angles, and symmetry. Understanding these classifications, especially for quadrilaterals, helps in identifying features like whether the shape is a kite, parallelogram, or trapezoid, each with unique properties.

Coordinate Geometry

Coordinate geometry involves representing geometric figures on a coordinate plane, where each point is defined by an ordered pair. This allows properties of figures such as distance, slope, and area to be calculated algebraically by using formulas derived from the coordinates.

Distance Formula

The distance formula, derived from the Pythagorean theorem, provides a method to determine the distance between two points on the coordinate plane. This formula is critical when calculating the lengths of sides in polygonal figures, which is essential for further determining properties like the perimeter.

Shoelace Formula

The Shoelace Formula is an algorithm used to calculate the area of a polygon when given the coordinates of its vertices. By arranging the coordinates in a systematic order and performing cross-multiplication, one can efficiently compute the area, even for irregular shapes.

Perimeter Calculation

Calculating the perimeter of a polygon involves summing the lengths of all its sides. By applying the distance formula to consecutive pairs of vertices, one can determine the individual side lengths, which are then added together to obtain the total perimeter.

Transcript

00:01 For problem number 13, it's the same as problem number 12, and also problems number 3 and 4 in this section.

00:14 So the first thing that we need to do is graph our coordinates, l -m -n -p.

00:19 They want us to identify what the polygon is, and then find the area and perimeter of the shape.

00:25 So the first thing that we need to do is graph l, so that is 7 -5, 1, 2, and then up 5, that is l.

00:38 M is 5 -0, n is 35, and p is 5 -10.

01:02 So what we look to have is a diamond, rhombus, one of the two.

01:15 So the way that we can determine what this shape actually is, is by finding the sides, find the distance of the points of the sides, finding the perimeters.

01:29 Oh my gosh, you have to laugh at yourself sometimes.

01:32 Finding the side links.

01:36 So in order to do this, we need to use the distance formula.

01:39 It doesn't matter what points you call one and two.

01:42 Our distance formula is, of course, d equals the square root.

01:49 I will actually write this down here.

01:52 D equals the square root, x1 minus x2 squared, plus y1 minus y2 squared.

02:04 So the first distance that i want to try to find is lm.

02:11 So lm, i'm going to let lb .1, mb .2, so 7 minus 5 squared, plus 5 minus 0 squared.

02:29 Now when i plug that into my calculator, i will get lm is equal to 5 .39.

02:42 So lm 5 .39.

02:53 Now of course this is not only to classify our shape, but this is also to help us find the perimeter.