What is the area, in the square units, of triangle KLM?
To find the area of triangle KLM, we first need to find the base and height of the triangle.
From the coordinates given:
K(1,1)
L(3,4)
M(5,1)
The base of the triangle is the distance between points K and M, which can be found using the distance formula:
Base = √ ( (5-1)^2 + (1-1)^2 )
Base = √ ( 4^2 + 0^2 )
Base = √16
Base = 4 units
The height of the triangle can be found by dropping a perpendicular line from point L to the base KM. This forms a right-angled triangle with base KM and height LM. Using the Pythagorean theorem:
LM = √ ( (3-1)^2 + (4-1)^2 )
LM = √ ( 2^2 + 3^2 )
LM = √ ( 4 + 9 )
LM = √13 units
Now, we can calculate the area of triangle KLM using the formula for the area of a triangle:
Area = 0.5 * Base * Height
Area = 0.5 * 4 * √13
Area = 2 * √13 square units
Therefore, the area of triangle KLM is approximately 7.21 square units.