A kite has vertices at [tex]\((2,4), (5,4), (5,1)\)[/tex], and [tex]\((0,-1)\)[/tex].

What is the approximate perimeter of the kite? Round to the nearest tenth.

A. 11.3 units

B. 13.6 units

C. 16.8 units

D. 20.0 units



Answer :

To determine the approximate perimeter of a kite with vertices at [tex]\((2, 4)\)[/tex], [tex]\((5, 4)\)[/tex], [tex]\((5, 1)\)[/tex], and [tex]\((0, -1)\)[/tex], we need to calculate the lengths of its four sides and then sum these lengths. Here are the detailed steps:

1. Calculate the distance between the vertices [tex]\((2, 4)\)[/tex] and [tex]\((5, 4)\)[/tex]:
These points share the same y-coordinate, so the distance is simply the difference in x-coordinates:
[tex]\[ \text{Distance} = \sqrt{(5 - 2)^2 + (4 - 4)^2} = \sqrt{3^2 + 0^2} = \sqrt{9} = 3.0 \][/tex]

2. Calculate the distance between the vertices [tex]\((5, 4)\)[/tex] and [tex]\((5, 1)\)[/tex]:
These points share the same x-coordinate, so the distance is simply the difference in y-coordinates:
[tex]\[ \text{Distance} = \sqrt{(5 - 5)^2 + (4 - 1)^2} = \sqrt{0^2 + 3^2} = \sqrt{9} = 3.0 \][/tex]

3. Calculate the distance between the vertices [tex]\((5, 1)\)[/tex] and [tex]\((0, -1)\)[/tex]:
[tex]\[ \text{Distance} = \sqrt{(0 - 5)^2 + (-1 - 1)^2} = \sqrt{(-5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29} \approx 5.385 \][/tex]

4. Calculate the distance between the vertices [tex]\((0, -1)\)[/tex] and [tex]\((2, 4)\)[/tex]:
[tex]\[ \text{Distance} = \sqrt{(2 - 0)^2 + (4 - (-1))^2} = \sqrt{2^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.385 \][/tex]

Next, we add these distances together to find the perimeter of the kite:
[tex]\[ \text{Perimeter} = 3.0 + 3.0 + 5.385 + 5.385 \approx 16.770 \][/tex]

Rounding this to the nearest tenth:
[tex]\[ \text{Perimeter} \approx 16.8 \text{ units} \][/tex]

Thus, the approximate perimeter of the kite is [tex]\(16.8\)[/tex] units. Therefore, the correct answer is:
[tex]\[ \boxed{16.8 \text{ units}} \][/tex]