what is the area of the polygon (1 point) 268, 70, 112, 400
To find the area of a polygon with the given coordinates, we first need to determine the coordinates of the vertices of the polygon.
The given coordinates are: (268, 70), (112, 400), and (400, ?).
To find the missing y-coordinate of the third vertex, we can calculate the slope of the line passing through the first two vertices:
slope = (400 - 70) / (400 - 268)
= 330 / 132
= 5 / 2
Using the slope and the first point (268, 70), we can find the y-coordinate of the third vertex:
400 = 70 + (5 / 2)(400 - 268)
400 = 70 + (5 / 2)(132)
400 = 70 + 330
400 = 400
Therefore, the coordinates of the third vertex are (400, 240).
Now that we have the coordinates of the vertices of the polygon, we can calculate the area using the shoelace formula:
Area = 1/2 |(268*400 + 112*240 + 400*70) - (70*112 + 400*400 + 240*268)|
Area = 1/2 |(107200 + 26880 + 28000) - (7840 + 160000 + 64320)|
Area = 1/2 |161080 - 233160|
Area = 1/2 |-72080|
Area = 36040
Therefore, the area of the polygon is 36040.