Question

what is the area of triangle abc? 3 square units 2.5 square units 3.5 square units 4 square units

Explanation:

Step1: Determine the base and height of the triangle

From the graph, for triangle \(ABC\), the base \(BC\) is \(2\) units (since the vertical distance between \(B\) and \(C\)) and the base is along the \(y -\)axis. The base \(b = 2\), and the horizontal distance (which is the height \(h\) with respect to base \(BC\)) from the \(y -\)axis to the line containing \(BC\) (measured along the \(x -\)axis) is \(3\) units. But wait, no - using the formula \(A=\frac{1}{2}\times base\times height\). If we consider \(BC\) as the base. The length of \(BC\) is \(2\) (counting the grid units: \(y\) - coordinate of \(B\) is \(4\), \(y\) - coordinate of \(C\) is \(2\), \(|4 - 2|=2\)), and the base of the triangle (the horizontal distance from the \(x\) - value of the line perpendicular to \(BC\)) is \(3\) (but no, wrong approach. Let's use the formula \(A=\frac{1}{2}\times base\times height\) correctly. If we assume the base \(b = 2\) (vertical side \(BC\)) and height \(h= 3\) (horizontal distance from the \(x\) - axis to the line \(BC\) in the relevant direction). Wait, no. Let's use the formula \(A=\frac{1}{2}\times base\times height\). Looking at the grid, if we take \(BC\) as the base. The length of \(BC\) is \(2\) (from \(y = 2\) to \(y = 4\) at \(x = 3\)). The height is \(3\) (from \(x=0\) to \(x = 3\)). But no, wait. Wait, the formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). If we consider the base \(BC\) (vertical side). The length of \(BC\) is \(2\) (counting the grid squares: \(4 - 2=2\)). The height is \(3\) (the horizontal distance from the \(y\) - axis to \(x = 3\)). But no, wrong. Wait, another approach: The coordinates (assuming \(C=(3,2)\), \(B=(3,4)\)). The base \(BC\) has length \(|4 - 2| = 2\). The height is the horizontal distance from the line \(x = 0\) to \(x=3\) (since the base \(BC\) is vertical). So \(A=\frac{1}{2}\times2\times3= 3\)

Answer:

3 square units