the coordinates for a triangular park has the vertices of (10.5), (15,5), (10,12). what is the area of the triangular park in square meters?
If you plot the points, you will see they form a right angle, with lengths 5 and 7. So, the area is 5*7/2 = 17.5
To find the area of a triangle, you can use the formula for the area of a triangle given its vertices. The formula is as follows:
A = 0.5 * |(x1 * (y2 - y3)) + (x2 * (y3 - y1)) + (x3 * (y1 - y2))|
Let's use this formula to find the area of the given triangular park with vertices (10.5), (15,5), and (10,12):
First, let's assign coordinates to each vertex:
Vertex 1: (x1, y1) = (10.5)
Vertex 2: (x2, y2) = (15, 5)
Vertex 3: (x3, y3) = (10, 12)
Next, substitute the values into the formula:
A = 0.5 * |(10.5 * (5 - 12)) + (15 * (12 - 10.5)) + (10 * (10.5 - 5))|
Now, calculate the expression within the absolute value:
A = 0.5 * |-63 + 15 + 52.5|
Simplify the expression within the absolute value:
A = 0.5 * |4.5|
Finally, calculate the absolute value and multiply by 0.5 to find the area:
A = 0.5 * 4.5
A = 2.25 square meters
Therefore, the area of the triangular park is 2.25 square meters.