Find the area of a triangle with vertices at A(0, 0, 0), B(1, 0, 0), and C(0, 1,
Practice Questions
Q1
Find the area of a triangle with vertices at A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0). (2023)
0.5
1
2
0
Questions & Step-by-Step Solutions
Find the area of a triangle with vertices at A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0). (2023)
Step 1: Identify the coordinates of the vertices of the triangle. The vertices are A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0).
Step 2: Determine the base of the triangle. The base can be the distance between points A and B. The distance is 1 unit (from (0,0) to (1,0)).
Step 3: Determine the height of the triangle. The height is the distance from point C to the line AB. Since C is at (0, 1, 0), the height is also 1 unit.
Step 4: Use the formula for the area of a triangle: Area = 0.5 * base * height.
Step 5: Substitute the values into the formula: Area = 0.5 * 1 * 1.
Step 6: Calculate the area: Area = 0.5 square units.
Area of a Triangle – The area of a triangle can be calculated using the formula Area = 0.5 * base * height, where the base and height are perpendicular to each other.
Coordinate Geometry – Understanding how to determine the vertices of a triangle in a 3D coordinate system and how to project them onto a 2D plane for area calculation.
