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

`Perimeter = 11 + √(13)`

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 = √((x_1 - x_2)^2 + (y_1 - y_2)^2)`

So we have that:

`WX = √((2 - 4)^2 + (3 - 6)^2) = √(13)`

`XY = √((4 - 7)^2 + (6 - 6)^2) = 3`

`YZ = √((7 - 7)^2 + (6 - 3)^2) = 3`

`WZ = √((2 - 7)^2 + (3 - 3)^2) = 5`

The perimeter is:

`Perimeter = WX + XY + YZ + WZ`

`Perimeter = √(13) + 3 + 3 + 5 =11 + √(13)`