Final answer:
To find the area of a triangle with given vertices, use the formula Area = 1/2 * base * height. Calculate the base and height by finding the distances between the points. Then, plug the values into the formula to find the area.
Step-by-step explanation:
To find the area of a triangle with vertices (0,0), (5,3), and (3,4), we can use the formula for the area of a triangle. The formula is: Area = 1/2 * base * height.
First, we need to determine the base and height of the triangle. The base can be found by calculating the distance between the points (0,0) and (5,3), which is 5 units. The height can be found by calculating the distance between the point (5,3) and the line passing through (0,0) and (3,4). Using the distance formula, we determine the height to be 2 units.
Now we can calculate the area of the triangle using the formula: Area = 1/2 * base * height. Plugging in the values, we get: Area = 1/2 * 5 * 2 = 5 square units. Therefore, the area of the triangle is 5 square units.