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: Identify base and height

The base of the triangle can be found by the horizontal distance between points Z(-1,13) and E(-1, - 23). The height can be found by the vertical distance from point Q(-18,3) to the line containing ZE. The length of the base $b$ is calculated as the absolute - value of the difference in the y - coordinates of Z and E. $b=\vert13-( - 23)\vert=\vert13 + 23\vert=36$. The height $h$ is the absolute - value of the difference in the x - coordinates of Q and Z (or Q and E since they have the same x - coordinate), $h=\vert-1-(-18)\vert=\vert-1 + 18\vert = 17$.

Step2: Apply area formula

The area formula for a triangle is $A=\frac{1}{2}bh$. Substitute $b = 36$ and $h = 17$ into the formula: $A=\frac{1}{2}\times36\times17$. First, $\frac{1}{2}\times36 = 18$, then $18\times17=306$.

Answer:

306