Question

calculating the area of a triangle
find the area of the triangle def
area = square units

Explanation:

Step1: Find the coordinates of points

Assume \(D(-9,8)\), \(E(9,-1)\), \(F(-9,-7)\)

Step2: Calculate the base length

The base \(DF\) is the vertical distance between \(D(-9,8)\) and \(F(-9,-7)\). Using the distance formula for vertical points (\(x_1 = x_2\)), \(DF=\vert8-(-7)\vert=\vert8 + 7\vert=15\)

Step3: Calculate the height

The height is the horizontal distance from \(E(9,-1)\) to the line \(x=-9\) (where \(DF\) lies). So the height \(h=\vert9-(-9)\vert=\vert9 + 9\vert = 18\)

Step4: Use the area formula for a triangle

The area formula of a triangle is \(A=\frac{1}{2}\times base\times height\). Substitute \(base = 15\) and \(height=18\) into the formula: \(A=\frac{1}{2}\times15\times18\)

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Answer:

\(135\)