Question

find the area of triangle abc.

Explanation:

Step1: Find the length of AB

Points A(4, -2) and B(8, -2) have the same y - coordinate, so the length of AB is the difference in the x - coordinates.
Length of AB = \(|8 - 4|=4\)

Step2: Find the height of the triangle

The height is the vertical distance from point C to the line AB. Since AB is horizontal (y=-2), the y - coordinate of C is 6 and the y - coordinate of AB is - 2. So the height h=\(|6-(-2)| = 8\)

Step3: Calculate the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, base = AB = 4 and height = 8.
\(A=\frac{1}{2}\times4\times8\)
\(A = 16\)

Answer:

16