one factor in flood safety along a levee is the area that will absorb water should the levee break the coordinates that make up the boundary area are (0,0) (2.8, 2.1) and (4.3)(4.4) what is the area of the land that would absorb the water
To find the area of the land that would absorb the water, we can use the Shoelace Formula or the Surveyor's Formula. Both formulas work by finding the area of a polygon given its coordinates.
Using the Shoelace Formula:
First, let's write down the coordinates of the given boundary area:
(0,0) (2.8, 2.1) (4.3, 4.4)
We will repeat the first coordinate at the end to close the polygon:
(0,0) (2.8, 2.1) (4.3, 4.4) (0,0)
Now, let's calculate the area:
Area = (1/2) × |(0×2.1 + 2.8×4.4 + 4.3×0) - (0×2.8 + 2.1×4.3 + 4.4×0)|
Area = (1/2) × |(0 + 12.32 + 0) - (0 + 9.03 + 0)|
Area = (1/2) × |12.32 - 9.03|
Area = (1/2) × 3.29
Area = 1.645 square units
Therefore, the area of the land that would absorb the water is approximately 1.645 square units.
To find the area of the land that would absorb the water, we can use the shoelace formula, also known as the Gauss's area formula. This formula calculates the area of a polygon given the coordinates of its vertices.
First, let's list the coordinates in clockwise order:
(0, 0), (2.8, 2.1), (4.3, 4.4)
Now, let's apply the shoelace formula:
Area = 1/2 * |(0 * 2.1 + 2.8 * 4.4 + 4.3 * 0) - (0 * 4.4 + 2.1 * 4.3 + 4.4 * 2.8)|
Simplifying:
Area = 1/2 * |(0 + 12.32 + 0) - (0 + 9.03 + 12.32)|
Area = 1/2 * |12.32 - 21.35|
Area = 1/2 * |-9.03|
Area = 4.515 square units
The area of the land that would absorb the water is approximately 4.515 square units.
To find the area of the land that would absorb the water, you need to use the coordinates of the boundary area and apply the shoelace formula. The shoelace formula, also known as the Gauss area formula or the surveyor's formula, calculates the area of an irregular polygon given its vertex coordinates.
Step 1: Arrange the coordinates in a clockwise or counterclockwise order.
The given coordinates are: (0,0), (2.8,2.1), and (4.3,4.4). Let's arrange them in counterclockwise order: (0,0), (2.8,2.1), and (4.3,4.4).
Step 2: Apply the shoelace formula.
The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) is given by:
Area = 0.5 * |(x1 * y2 + x2 * y3 + ... + xn * y1) - (x2 * y1 + x3 * y2 + ... + xn * y1 + x1 * yn)|
Using the coordinates: (0,0), (2.8,2.1), and (4.3,4.4), we can substitute the values into the shoelace formula:
Area = 0.5 * |(0 * 2.1 + 2.8 * 4.4 + 4.3 * 0) - (2.8 * 0 + 4.3 * 2.1 + 0 * 4.4)|
Simplifying the expression:
Area = 0.5 * |(0 + 12.32 + 0) - (0 + 9.03 + 0)|
Area = 0.5 * |12.32 - 9.03|
Area = 0.5 * 3.29
Area = 1.645 square units
Therefore, the area of the land that would absorb the water is approximately 1.645 square units.