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.
What is the area, in the square units, of triangle KLM?
1 answer