Question

the coordinate plane shows triangle abc. what is the area of the triangle? enter your answer in the box. square units

Explanation:

Step1: Identify base and height

By observing the graph, assume base is along the horizontal - direction and height is along the vertical - direction. The base \(b\) of the triangle can be found by calculating the horizontal distance between two points. Let's assume the base is the distance between points \(B(6,0)\) and \(A(2,4)\) projected horizontally. The height \(h\) is the vertical distance from the third point \(C(6,6)\) to the line containing the base. The base \(b = 4\) (from \(x = 2\) to \(x = 6\)) and the height \(h= 3\) (from \(y = 3\) (the \(y\) - coordinate of the line containing the base - like a horizontal line through \(A\) and \(B\) in a sense) to \(y = 6\)).

Step2: Apply area formula

The area formula of a triangle is \(A=\frac{1}{2}bh\). Substitute \(b = 4\) and \(h = 3\) into the formula. \(A=\frac{1}{2}\times4\times3\).

Step3: Calculate the area

\(A = 6\).

Answer:

6