Question

The coordinates of three vertices of a triangle are (4, 0), (5, 3), and (0, 0).

What is the area of the triangle?

Answer 1

The area of the triangle with given coordinates is sqrt(340)/2 square units.

Step-by-step explanation:

To find the area of a triangle, we can use the formula:

Area = 1/2 * base * height

In this case, the coordinates of the three vertices of the triangle are (4, 0), (5, 3), and (0, 0). We can use the distance formula to find the length of the base and the height:

Base = distance between (4, 0) and (5, 3)

Height = distance between (0, 0) and (5, 3)

Using the distance formula:

Base = sqrt((5 - 4)^2 + (3 - 0)^2) = sqrt(1 + 9) = sqrt(10)

Height = sqrt((5 - 0)^2 + (3 - 0)^2) = sqrt(25 + 9) = sqrt(34)

Now we can substitute these values into the formula:

Area = 1/2 * sqrt(10) * sqrt(34)

Area = 1/2 * sqrt(340) = sqrt(340)/2

So the area of the triangle is sqrt(340)/2 square units.

Answer 2

Check the picture below.