Question

find the area of the figure.

Explanation:

Step1: Identify base and height

The base of the triangle is the horizontal distance between the two bottom - most points. The two bottom - most points are \((2,-4)\) and \((4,-4)\), so the base \(b = 4 - 2=2\). The height \(h\) is the vertical distance from the top vertex \((2,2)\) to the line \(y = - 4\), so \(h=2-(-4)=6\).

Step2: Apply area formula

The area formula for a triangle is \(A=\frac{1}{2}bh\). Substitute \(b = 2\) and \(h = 6\) into the formula: \(A=\frac{1}{2}\times2\times6\).

Step3: Calculate the area

\(A = 6\).

Answer:

6