Respuesta :
The area of Eunice's kite is [tex]2\sqrt{58}[/tex].
What is the kite?
A kite is a tethered heavier-than-air or lighter-than-air craft with wing surfaces that react against the air to create lift and drag forces.
Eunice is flying a kite with vertices at points A(0, 0), B(0, 4), C(7, 7), and D(4, 0).
If the diagonals in a quadrilateral are perpendicular to each other then the area is one-half of the product of the diagonals.
All Kites and rhombi fall in this category.
By the distance formula;
[tex]\rm AB =\sqrt{(0-0)^2+(4-0)^2} =\sqrt{0+16} =\sqrt{16} =4\\\\BC =\sqrt{(7-0)^2+(7-4)^2} =\sqrt{49+9} =\sqrt{58} \\\\CD =\sqrt{(4-7)^2+(0-7)^2} =\sqrt{49+9} =\sqrt{58}\\\\AD =\sqrt{(0-0)^2+(4-0)^2} =\sqrt{0+16} =\sqrt{16} =4\\[/tex]
The area of Eunice's kite is;
[tex]\rm Area = \dfrac{1}{2} \times AB \times BC\\\\Area =\dfrac{1}{2} \times 4 \times \sqrt{58} \\\\Area =2\sqrt{58}[/tex]
Hence, the area of Eunice's kite is [tex]2\sqrt{58}[/tex].
Learn more about kites here;
https://brainly.com/question/3507003
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