Question

Find the perimeter of trapezoid WXYZ with vertices W(2, 3), X(4, 6), Y(7, 6), and Z(7,3). Leave your answer in simplest radical form.

Answer 1

Answer:

$Perimeter = 11 + \sqrt{13}$

Step-by-step explanation:

To find the perimeter of WXYZ we need to find the length of all four sides: WX, XY, YZ and WZ.

To find the length of each side, we can use the formula for the distance of two points:

$distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

So we have that:

$WX = \sqrt{(2 - 4)^2 + (3 - 6)^2} = \sqrt{13}$

$XY = \sqrt{(4 - 7)^2 + (6 - 6)^2} = 3$

$YZ = \sqrt{(7 - 7)^2 + (6 - 3)^2} = 3$

$WZ = \sqrt{(2 - 7)^2 + (3 - 3)^2} = 5$

The perimeter is:

$Perimeter = WX + XY + YZ + WZ$

$Perimeter = \sqrt{13} + 3 + 3 + 5 =11 + \sqrt{13}$