Question

what is the area of the parallelogram?

Explanation:

Step1: Find the base length

The base of the parallelogram is the horizontal distance between two points on the same - height. Consider the points \((-6,-3)\) and \((5,-3)\). The length of the base \(b\) is calculated using the distance formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) on a horizontal line (\(y_1 = y_2\)): \(b=\vert x_2 - x_1\vert\). Here, \(x_1=-6\), \(x_2 = 5\), so \(b=\vert5-(-6)\vert=\vert5 + 6\vert=11\).

Step2: Find the height

The height \(h\) of the parallelogram is the vertical distance between two points on the base - parallel lines. Consider the points \((-6,-3)\) and \((-6,1)\). The height \(h\) is calculated using the distance formula for two points \((x_1,y_1)\) and \((x_1,y_2)\) on a vertical line (\(x_1=x_2\)): \(h=\vert y_2 - y_1\vert\). Here, \(y_1=-3\), \(y_2 = 1\), so \(h=\vert1-(-3)\vert=\vert1 + 3\vert=4\).

Step3: Calculate the area

The area \(A\) of a parallelogram is given by the formula \(A = b\times h\). Substitute \(b = 11\) and \(h = 4\) into the formula, we get \(A=11\times4 = 44\).

Answer:

44