Questions: Kite WXYZ is graphed on a coordinate plane. What is the approximate perimeter of the kite? Round to the nearest tenth. 10.6 units 11.5 units 14.0 units 16.2 units

Solution Steps

The coordinates of the vertices of the kite WXYZ are: W(1, 1) X(3, 4) Y(5, 1) Z(3, -3)

We can use the distance formula to find the lengths of the sides. The distance formula is $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

WX = $\sqrt{(3 - 1)^2 + (4 - 1)^2} = \sqrt{2^2 + 3^2} = \sqrt{4 + 9} = \sqrt{13}$

XY = $\sqrt{(5 - 3)^2 + (1 - 4)^2} = \sqrt{2^2 + (-3)^2} = \sqrt{4 + 9} = \sqrt{13}$

YZ = $\sqrt{(3 - 5)^2 + (-3 - 1)^2} = \sqrt{(-2)^2 + (-4)^2} = \sqrt{4 + 16} = \sqrt{20}$

ZW = $\sqrt{(1 - 3)^2 + (1 - (-3))^2} = \sqrt{(-2)^2 + 4^2} = \sqrt{4 + 16} = \sqrt{20}$

Perimeter = WX + XY + YZ + ZW = $\sqrt{13} + \sqrt{13} + \sqrt{20} + \sqrt{20} = 2\sqrt{13} + 2\sqrt{20} \approx 2(3.6) + 2(4.47) \approx 7.2 + 8.94 \approx 16.14$

Final Answer