A kite has diagonals 5.3 ft and 6 ft. What is the area of the kite?
(1 point)
Responses
5.65 ft²
5.65 ft²
15.9 ft²
15.9 ft²
31.8 ft²
31.8 ft²
22.6 ft²
To find the area of the kite, we first need to find the lengths of the two perpendicular diagonals.
Since the diagonals of a kite are perpendicular and intersect each other at a 90-degree angle, we can use the Pythagorean theorem to find the lengths of the diagonals.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse.
Let's call the length of one diagonal x and the length of the other diagonal y. Given that the lengths of the diagonals are 5.3 ft and 6 ft, we have:
x^2 + y^2 = 5.3^2
x^2 + y^2 = 28.09 ..........(1)
x^2 + y^2 = 6^2
x^2 + y^2 = 36 .............(2)
Now, we can set up the system of equations:
x^2 + y^2 = 28.09
x^2 + y^2 = 36
Subtracting equation (2) from equation (1) gives:
x^2 + y^2 - (x^2 + y^2) = 28.09 - 36
0 = -7.91
This means that the system of equations is inconsistent and does not have a solution. Therefore, the given lengths of the diagonals do not correspond to the sides of a kite.
Hence, we cannot find the area of the kite with the given information.