Area of rectilinear figures using shoelace method

Welcome to our YouTube video on the shoelace method for finding the area of rectilinear figures!

In this video, we will be discussing a powerful technique for finding the area of rectilinear figures, which are figures made up of straight lines and angles. This method is called the shoelace method, and it gets its name from the way in which it works – just like tying shoelaces!

To begin, let’s consider a simple example. Suppose we have a rectilinear figure with vertices at the points (1,1), (3,4), (5,2), and (2,1). Our goal is to find the area of this figure.

The shoelace method works by first listing the coordinates of the vertices in a specific order, either clockwise or counterclockwise. Let’s list the coordinates of our example in counterclockwise order:

(1,1)
(3,4)
(5,2)
(2,1)

Next, we “lace up” the vertices by multiplying each x-coordinate by the y-coordinate of the next vertex, and subtracting each y-coordinate by the x-coordinate of the next vertex. For our example, we get:

(1,1) * (4,3) = 4
(3,4) * (5,2) = -8
(5,2) * (2,1) = -9
(2,1) * (1,1) = 1

To find the area of the rectilinear figure, we add up these products and take half the absolute value of the result:

|(4 + (-8) + (-9) + 1)| / 2 = 11 / 2 = 5.5

So, the area of our rectilinear figure is 5.5 square units.

Let’s try another example to see how the shoelace method works. Suppose we have a rectilinear figure with vertices at the points (2,1), (4,4), (6,1), and (5,-1). Our goal is to find the area of this figure.

Listing the coordinates in counterclockwise order, we get:

(2,1)
(4,4)
(6,1)
(5,-1)

Multiplying the coordinates and “lacing up” the vertices, we get:

(2,1) * (4,4) = 6
(4,4) * (6,1) = -10
(6,1) * (5,-1) = -11
(5,-1) * (2,1) = 7

Adding up these products and taking half the absolute value, we get:

|(6 + (-10) + (-11) + 7)| / 2 = 4

So, the area of our rectilinear figure is 4 square units.

The shoelace method is a powerful tool for finding the area of rectilinear figures, as it can be used for any number of vertices and any shape. It works by breaking down the shape into triangles and adding up the areas of the triangles. This can be particularly useful when dealing with irregular shapes or shapes that are difficult to break down into simpler shapes.

In conclusion, the shoelace method is a useful technique for finding the area of rectilinear figures, and it can be easily applied to any shape. By listing the coordinates in a specific order and “lacing up” the vertices, we can quickly and accurately find the area of a rectilinear figure