1)How to find the area bounded by the 4 points in a coordinate?
2)what is the formula?
3)how the formula related to that?
The area can be found by using cross multiplication of elements in a rectangular matrix formed by the coordinates of the 4 (or any number) points.
Let P be a 5x2 matrix, where the columns represnt the x and y coordinates.
Rows 1 to 4 represent the (x,y) ordered pairs of the 4 points, and the fifth row is a repetition of the fist row.
The area is obtained by the following formula:
Area=|(ΣP(i,1)*P(i+1,2)-P(i+1,1)*P(i,2))|/2 for i=1 to 4.
Example:
Find area of
(1,2)
(2,4)
(1,4)
(5,5)
Repeat the first row:
(1,2)
(2,4)
(1,4)
(5,5)
(1,2)
Form sum
Area=|(1*4-2*2+2*4-1*4+1*5-5*4+5*2-1*5)|/2
=3
1) Ah, finding the area bounded by four points, sounds like geometry got a little edgy! Well, you can find the area by considering the points as vertices of a quadrilateral. One approach is to divide it into two triangles and then find their individual areas.
2) Now, the formula for finding the area of a triangle is (1/2) * base * height. So, you can apply this formula to both triangles formed by the four points.
3) As for how the formula relates to finding the area bounded by the four points, well, think of it like this: by dividing the quadrilateral into two triangles, you get two separate areas that add up to give you the total area. So, by applying the formula for the area of a triangle to each triangle, you can determine the overall bounded area. It's like finding the humor in a joke - you break it down into smaller parts to understand the whole picture!
1) To find the area bounded by four points in a coordinate system, you can follow these steps:
Step 1: Identify the four points in the coordinate system. Let's call them A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4).
Step 2: Calculate the lengths of two sides of the rectangle formed by these points. For example, if AB and AD are the sides of the rectangle, you can use the distance formula to calculate their lengths:
Length AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Length AD = sqrt((x4 - x1)^2 + (y4 - y1)^2)
Step 3: Multiply the length of AB by the length of AD to find the area of the rectangle:
Area = Length AB * Length AD
Step 4: If the rectangle is not a perfect rectangle, there may be triangles or other irregular shapes within the rectangle. You will need to calculate the areas of these additional shapes separately and subtract them from the total area calculated in step 3.
2) The formula to find the area bounded by four points in a coordinate system is:
Area = Length AB * Length AD
Where Length AB represents the length of one side of the rectangle formed by the points, and Length AD represents the length of the adjacent side of the rectangle.
3) The formula is related to finding the area of a rectangle by multiplying the lengths of two adjacent sides. In this case, the lengths are determined by calculating the distances between the given points using the distance formula. By applying this formula, you can determine the total area within the rectangle formed by the four points.
To find the area bounded by four points in a coordinate system, you can use the shoelace formula (also known as Gauss's area formula or the surveyor's formula).
Here's how you can use the shoelace formula to find the area:
1) Arrange the four points in clockwise or counterclockwise order.
2) Assign them coordinates: Let's say the coordinates of the four points are (x1, y1), (x2, y2), (x3, y3), and (x4, y4).
3) Multiply each x-coordinate with its adjacent y-coordinate and each y-coordinate with its adjacent x-coordinate.
4) Sum up the products obtained in step 3.
5) Take the absolute value of this sum divided by 2, and that will be the area bounded by the four points.
The formula for finding the area using the shoelace formula is:
Area = |(x1y2 + x2y3 + x3y4 + x4y1) - (x2y1 + x3y2 + x4y3 + x1y4)| / 2
In this formula, the products of the adjacent coordinates are summed up and then subtracted from the sum of the products of the opposite adjacent coordinates.
The shoelace formula is related to finding the area of a polygon by utilizing its vertices. By multiplying the coordinates and summing them up, the formula calculates the area enclosed by the sides of the polygon. The reason it is called the shoelace formula is because the arrangement of the terms in the formula resembles the pattern made by lacing up a shoe.