The figure below shows graphed on the coordinate plane.
Triangle X-Y-Z with a perpendicular line P-Y from vertex Y on line X-Z forming two right triangles X-Y-P and Z-Y-P. Triangle X-Y-Z has its vertices X at (0, 8), Y at (6, 8) and Z at (5, 3).
What is the area of ?
A
.
15 square units
B.
square units
C.
30 square units
D.
square units
To find the area of triangle X-Y-Z, we can first find the base and height of the triangle.
The base of the triangle is the distance between points X and Z, which can be found using the distance formula:
Base = sqrt((5-0)^2 + (3-8)^2)
Base = sqrt(25 + 25)
Base = sqrt(50)
The height of the triangle is the perpendicular distance from vertex Y to line X-Z, which is the y-coordinate of point Y (since we only need the vertical distance).
Height = 8
Now we can find the area of the triangle using the formula for the area of a triangle:
Area = 0.5 * Base * Height
Area = 0.5 * sqrt(50) * 8
Area = 0.5 * 5sqrt(2) * 8
Area = 20sqrt(2)
Therefore, the area of triangle X-Y-Z is 20sqrt(2) square units. The answer is not listed, so it might be a good idea to double check the calculations to confirm.