Question

calculate the area of the triangle
a =
done

Explanation:

Step1: Find the base length

The two points \((-2,6)\) and \((-2,0)\) have the same \(x -\)coordinate. The distance between them (base \(b\)) is calculated using the distance formula for points \((x_1,y_1)\) and \((x_2,y_2)\) when \(x_1 = x_2\): \(b=\vert y_1 - y_2\vert\).
So, \(b=\vert6 - 0\vert=6\).

Step2: Find the height

The \(x -\)coordinate of the base - related points is \(x=-2\), and the third point is \((7,-5)\). The height \(h\) is the horizontal distance between \(x=-2\) and \(x = 7\). Using the formula \(h=\vert x_1 - x_2\vert\) (since it's a horizontal distance in a coordinate - plane for calculating the area of this triangle), \(h=\vert7-(-2)\vert=\vert7 + 2\vert=9\).

Step3: Calculate the area

The area formula for a triangle is \(A=\frac{1}{2}\times b\times h\).
Substitute \(b = 6\) and \(h=9\) into the formula: \(A=\frac{1}{2}\times6\times9\).
First, \(6\times9 = 54\), then \(\frac{1}{2}\times54=27\).

Answer:

\(27\)