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 is the horizontal distance between \(O(1, - 3)\) and \(I(7,-3)\). Using the distance formula for points \((x_1,y_1)\) and \((x_2,y_2)\) on a horizontal line (\(y_1 = y_2\)), the base \(b=\vert x_2 - x_1\vert=\vert7 - 1\vert = 6\). The height \(h\) is the vertical distance from the line \(y=-3\) to the point \(H(1,8)\), so \(h=\vert8-(-3)\vert = 11\).

Step2: Apply triangle - area formula

The area formula of a triangle is \(A=\frac{1}{2}bh\). Substitute \(b = 6\) and \(h = 11\) into the formula: \(A=\frac{1}{2}\times6\times11\).
\[A = 33\]

Answer:

33