Question

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

Answer 1

Answer-

Perimeter of the kite is 16.2 units

Solution-

As WXYZ is a kite, so two disjoint pairs of consecutive sides are congruent, i.e WX=XY and WZ=ZY

So, perimeter of the kite WXYZ is,

$=2(\overline{WX}+\overline{WZ})$

And

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

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

So, perimeter will be,

$P=2(\sqrt{13}+\sqrt{20})=16.15\approx 16.2\ units$

Answer 2

Answer:

D. 16.2 units.

Step-by-step explanation:

We have been given an image of a kite on coordinate plane and we are asked to find the perimeter of our given kite.

Since we know that a kite has two disjoint pairs of congruent consecutive sides, so the perimeter of our given kite will be 2 times the sum of side XY and YZ.

To find the length of sides XY and YZ we will use distance formula.

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

Upon substituting coordinates of point X and Y in above formula we will get,

$\text{Distance between point X and Y}=\sqrt{(3-5)^2+(4-1)^2}$

$\text{Distance between point X and Y}=\sqrt{(-2)^2+(3)^2}$

$\text{Distance between point X and Y}=\sqrt{4+9}$

$\text{Distance between point X and Y}=\sqrt{13}$

Now similarly we will find the length of segment YZ.

$\text{Distance between point Y and Z}=\sqrt{(5-3)^2+(1--3)^2}$

$\text{Distance between point Y and Z}=\sqrt{(2)^2+(1+3)^2}$

$\text{Distance between point Y and Z}=\sqrt{4+(4)^2}$

$\text{Distance between point Y and Z}=\sqrt{4+16}$

$\text{Distance between point Y and Z}=\sqrt{20}$

$\text{Distance between point Y and Z}=2\sqrt{5}$

$\text{Perimeter of kite WXYZ}=2(XY+YZ)$

$\text{Perimeter of kite WXYZ}=2(\sqrt{13}+2\sqrt{5})$

$\text{Perimeter of kite WXYZ}=2(3.6055512754639893+4.4721359549995794)$

$\text{Perimeter of kite WXYZ}=2(8.0776872304635687)$

$\text{Perimeter of kite WXYZ}=16.1553744609271374\approx 16.2$

Therefore, the perimeter of the kite WXYZ is 16.2 units and option D is the correct choice.