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?%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A1.65 mi²%0D%0A1.65 mi²%0D%0A%0D%0A9.03 mi²%0D%0A9.03 mi²%0D%0A%0D%0A1.1 mi²%0D%0A1.1 mi²%0D%0A%0D%0A10.68 mi²
To find the area of the land that would absorb the water, we can use the shoelace formula (also known as Gauss's area formula) for calculating the area of a polygon. The formula states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) is:
A = | (x1 * y2 + x2 * y3 + ... + xn * y1) - (y1 * x2 + y2 * x3 + ... + yn * x1)| / 2
Using the given coordinates: (0, 0), (2.8, 2.1), and (4.3, 4.4), we can calculate the area as follows:
A = | (0 * 2.1 + 2.8 * 4.4 + 4.3 * 0) - (0 * 4.4 + 2.1 * 4.3 + 4.4 * 0) | / 2
= | (0 + 12.32 + 0) - (0 + 9.03 + 0) | / 2
= | 12.32 - 9.03 | / 2
= 3.29 / 2
= 1.645
Therefore, the area of the land that would absorb the water is approximately 1.645 square miles.
To find the area of the land that would absorb the water, we can use the Shoelace formula, also known as the Gauss Area Formula. Here are the steps to calculate it:
1. Write down the given coordinates in clockwise order. In this case, the coordinates are:
(0, 0), (2.8, 2.1), and (4.3, 4.4).
2. Duplicate the first coordinate at the end of the list. So, the new list becomes:
(0, 0), (2.8, 2.1), (4.3, 4.4), (0, 0).
3. Multiply the x-coordinate of each coordinate with the y-coordinate of the next coordinate in the list.
(0 * 2.1) + (2.8 * 4.4) + (4.3 * 0) = 5.88
4. Multiply the y-coordinate of each coordinate with the x-coordinate of the next coordinate in the list.
(0 * 2.8) + (2.1 * 4.3) + (4.4 * 0) = 9.03
5. Subtract the sum of the results from step 3 from the sum of the results from step 4. Take the absolute value of the result.
|9.03 - 5.88| = 3.15
6. Divide the result from step 5 by 2 to get the final area.
3.15 / 2 = 1.575 mi²
So, the area of the land that would absorb the water is approximately 1.575 mi².
To calculate the area of the land that would absorb the water, we can use the Shoelace formula, also known as the Surveyor's formula.
Let's label the given coordinates as (x1, y1), (x2, y2), and (x3, y3).
(x1, y1) = (0, 0)
(x2, y2) = (2.8, 2.1)
(x3, y3) = (4.3, 4.4)
Using the Shoelace formula, the area is given by:
Area = 1/2 * |(x1*y2 + x2*y3 + x3*y1) - (y1*x2 + y2*x3 + y3*x1)|
Area = 1/2 * |(0*2.1 + 2.8*4.4 + 4.3*0) - (0*4.4 + 2.1*4.3 + 4.4*2.8)|
Area = 1/2 * |(0 + 12.32 + 0) - (0 + 9.03 + 12.32)|
Area = 1/2 * |-3.71 - 21.35|
Area = 1/2 * |-25.06|
Area = 1/2 * 25.06
Area = 12.53 mi²
Therefore, the area of the land that would absorb the water is approximately 12.53 mi².