Question

the graph shows the vertices of a triangle. determine the area of the triangle. enter the unknown segment length(s), then calculate the area of the polygon. area of the triangle: square units

Explanation:

Step1: Find the base and height

Assume the base \(b\) is the horizontal distance between \(x -\)coordinates of two points. Let's take the points \(J(2,-2)\) and \(I(14, - 6)\). The base \(b=\vert14 - 2\vert=12\).
The height \(h\) is the vertical distance from the line containing \(JI\) to the third vertex. We can use the formula for the area of a triangle \(A=\frac{1}{2}\times b\times h\). By counting the grid - squares (or using the perpendicular distance concept in coordinate geometry), the height \(h = 4\).

Step2: Calculate the area

Using the formula \(A=\frac{1}{2}\times b\times h\), substitute \(b = 12\) and \(h=4\).
\(A=\frac{1}{2}\times12\times4\)
\(A = 24\)

Answer:

\(24\)