Question

what is the area of a parallelogram whose vertices are ( a(-1,12) ), ( b(13,12) ), ( c(2,-5) ), and ( d(-12,-5) )? enter your answer in the box units²

Explanation:

Step1: Calculate the base length

The \(y\) - coordinates of points \(A(-1,12)\) and \(B(13,12)\) are the same. Using the distance formula \(d=\vert x_2 - x_1\vert\) for points on a horizontal line (\(y = y_1=y_2\)), the base \(b=\vert13-(-1)\vert=\vert13 + 1\vert=14\).

Step2: Calculate the height

The \(y\) - coordinates of points \(B(13,12)\) and \(C(2,-5)\). Using the distance formula \(d=\vert y_2 - y_1\vert\) for a vertical distance (since the base is horizontal), the height \(h=\vert12-(-5)\vert=\vert12 + 5\vert=17\).

Step3: Calculate the area of the parallelogram

The area formula of a parallelogram is \(A = b\times h\). Substitute \(b = 14\) and \(h=17\) into the formula: \(A=14\times17 = 238\).

Answer:

\(238\)