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